Name: ERG 2022
Start: 2022-07-25T06:00:00+02:00
End: 2022-07-29T14:45:00+02:00
Location: No location set

ERG 2022

from Monday 25 July 2022 (06:00) to Friday 29 July 2022 (14:45)

Monday 25 July 2022

06:00 18:00 - 21:00 Welcome Reception & Poster Discussion
18:00 - 21:00 Welcome Reception & Poster Discussion
06:00 - 07:00

08:55 Welcome
Welcome
08:55 - 09:00
09:00 Positivity bounds in Effective Field Theories - Scott Melville
Positivity bounds in Effective Field Theories
- Scott Melville
09:00 - 09:45
09:45 From Random Tensors to Tensor Field Theory - Razvan Gurau
From Random Tensors to Tensor Field Theory
- Razvan Gurau
09:45 - 10:30
The latest addition to the family of large N field theories is tensor field theory built on the melonic large N limit of random tensors. This large N limit is richer than the vector large N limit but more amenable to analytic computations that the planar one. In this talk I will present an overview of the main results obtained on tensor field theories over the past several years and comment on their implications for the future.
10:30 Break
Break
10:30 - 11:00
11:00 Information theory and real space RG - Zohar Ringel
Information theory and real space RG
- Zohar Ringel
11:00 - 11:45
11:45 Functional RG for zero- and one-dimensional Fermi systems - Volker Meden
Functional RG for zero- and one-dimensional Fermi systems
- Volker Meden
11:45 - 12:30
I present an overview of our recent applications of funtional RG for zero- and one-dimensional many-fermion systems. The vertex expansion scheme with the two-particle interaction U being the small parameter is used. Equilibrium as well as nonequilibrium situations are considered. Several questions are tackled. Can one describe phase transitions which occur at finite U? If so, what is the role of the self-energy feedback and that of the two-particle vertex? Does the breaking of current conservation in nonequilibrium situations with a frequency dependent self-energy render the corresponding results useless right away? Can one use functional RG to study interacting (topological) insulators? Is it possible to extend functional RG to the realm of pseudo-Hermitian quantum many-body problems?
12:30 Lunch break
Lunch break
12:30 - 14:30
14:30 Extended symmetries - Stefan Floerchinger
Extended symmetries
- Stefan Floerchinger
14:30 - 14:55
Extended symmetry transformations do not leave the action fully invariant, but change it by a term linear in field expectation values or known composite fields. I will discuss how this leads to a modified version of Noethers theorem with currents that are conserved up to known terms. I will also discuss how an extended version of Galilei boost symmetry allows to close and solve renormalization group equations for cosmological large-scale structure formation in certain regimes.
SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model - Pietro Maria Bonetti
SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
- Pietro Maria Bonetti
14:30 - 14:55
We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo Néel or spiral magnetic order below a density dependent transition temperature $T^∗$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are applicable for a weak or moderate Hubbard interaction. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-Tc cuprates: a strong reduction of charge carrier density, a spin gap, Fermi arcs, and electronic nematicity.
14:55 Quantum Gravity Amplitudes From First Principles - Benjamin Knorr
Quantum Gravity Amplitudes From First Principles
- Benjamin Knorr
14:55 - 15:20
Renormalization group and probability theory: distribution of the order parameter at criticality - Ivan Balog
Renormalization group and probability theory: distribution of the order parameter at criticality
- Ivan Balog
14:55 - 15:20
Authors: Ivan Balog, Adam Rançon, Bertrand Delamotte; The question of probabilistic interpretation of the renormalization group has been around since the beginning of the subject of the renormalization group in the '70 [1], yet to this day no systematic approach exists for making practical calculations in cases when constituents of the system are strongly correlated, e.g. approaching criticality. Using functional renormalization group and the effective average action formalism [2], we write down a flow equation for the rate function $I(m)$, which determines the scaling function of the critical distribution of the order parameter $P(m)$, $I(m)=-ln(P(m))$. We show that $I$ is a universal function parametrized by $\zeta=\xi/L$ characterizing the approach to criticality. Monte Carlo results for different $\zeta=\xi/L$ collapse closely to the rate functions for different $\zeta$ determined from the renormalization group. For all cases when $\zeta>1$ the shape of the rate function is largely similar, yet not identical, to the shape of the fixed point (dimensionless) effective potential, featuring concavity near the origin. [1] G. Jona-Lasinio: Il Nuovo Cimento, 26, 99 (1975) [2] J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep. 363, 223 (2002).
15:20 Invariant Renormalization-Group improvement in General Relativity - Aaron Held
Invariant Renormalization-Group improvement in General Relativity
- Aaron Held
15:20 - 15:45
Renormalization-Group (RG) improvement has been applied to capture the effect of gravitational quantum corrections on cosmological and black-hole spacetimes. In this talk, I will use an algebraically complete set of curvature invariants to establish that (i) RG improvement at the level of the metric (or the equations of motion) is coordinate-dependent, while (ii) RG improvement at the level of curvature invariants (or the action) is coordinate-independent. Spherically-symmetric and axially-symmetric black-hole spacetimes serve as concrete and physically relevant examples.
The long-range XY model and other examples of exotic BKT scaling - Nicolo Defenu
The long-range XY model and other examples of exotic BKT scaling
- Nicolo Defenu
15:20 - 15:45
The two dimensional classical $XY$ model is characterised by the the presence, in the short-range regime, of a line of RG fixed points, which gives rise to the celebrated Berezinskii - Kosterlitz - Thouless (BKT) phenomenology. We will discuss the deformation of the BKT scaling caused by the inclusion of power-law decaying couplings, yielding a coexistence of spontaneously symmetry broken (SSB) and BKT phases in the phase diagram. Perturbative RG arguments imply that the SSB phenomenology observed in this model is described by a novel form of universality. Finally, in the last part of the talk, we are gonna extend our description of BKT scaling outside of the equilibrium world and consider the BKT scaling generated by the inclusion of non-Hermitian terms in the model Hamiltonian.
15:45 Break
Break
15:45 - 16:15
16:15 Gravity-mediated matter scattering amplitudes from the effective action - Chris Ripken
Gravity-mediated matter scattering amplitudes from the effective action
- Chris Ripken
16:15 - 16:35
One of the goals of the Asymptotic Safety program for gravity is to compute the effective action at k=0. However, given such an action, what are the concrete physical predictions that we can derive from it? Generically, the renormalization group will generate an infinite number of interactions in the effective action. It is therefore an interesting question which interactions can arise, and how they affect physical observables. In this talk, I will present a classification scheme to parameterize the infinitely many interactions using form factors. These take into account the full momentum-dependence of propagators and vertices. Using 2-to-2 scattering processes involving scalars and photons as a starting point, I will show how to derive the most general scattering amplitudes and cross-sections from the effective action. Taking the low-energy limit, this allows to parameterize the smoking gun signals for quantum gravity in these observables.
Precision calculation with FRG: the planar Bose gas as an example - Nicolas Dupuis
Precision calculation with FRG: the planar Bose gas as an example
- Nicolas Dupuis
16:15 - 16:35
16:35 Dimensional reduction along the RG flow in combinatorially non-local field theories - Johannes Thürigen
Dimensional reduction along the RG flow in combinatorially non-local field theories
- Johannes Thürigen
16:35 - 16:55
Combinatorially non-local interactions are at the heart of matrix and tensor theories as well as non-commutative field theory. Interestingly, for theories on a compact domain their renormalization group equations are non-autonomous in the momentum scale. We show that this should be regarded not as an issue but as a feature of such theories leading to a reduction of the effective dimension of the field theory along the renormalization group flow. We illustrate this with the example of a field theory with tensorial symmetry using the functional renormalization group in the cyclic-melonic potential approximation. While this yields a dimensional flow on compact domain, we also find a new phase structure with hints for an asymptotic safe fixed point in the large-volume limit.
TU^2FRG - a scalable approach for TUFRG in generic fermionic models - Jonas Hauck
TU^2FRG - a scalable approach for TUFRG in generic fermionic models
- Jonas Hauck
16:35 - 16:55
Describing the emergence of phases of matter is one of the central challenges in physics. The main complication is the tremendous computational effort required to investigate real materials. Therefore, approximations to enable accurate and fast calculations are of central importance to deepening our understanding of phases of matter. Here, we present a new truncated unity (TU) approach unifying real- and momentum-space TUFRG in a symmetry-preserving fashion, called TU$^2$FRG. This formalism significantly improves the scaling compared to conventional momentum (TU)FRG when applied to large unit-cell models and models without translational symmetry. To showcase its predictive power, we study the topological edge modes in the superconducting phase of graphene.
16:55 --
--
16:55 - 17:15
Functional RG for strongly interacting Hubbard model' - Demetrio Vilardi
Functional RG for strongly interacting Hubbard model'
- Demetrio Vilardi
16:55 - 17:15
17:15

17:15 - 17:20
17:20 Poster session
Poster session
17:20 - 18:35
Contributions

17:20 Information theoretic regulators for complex systems with multiple notions of scale - Adam Kline

17:20 Phase Transitions in Yukawa Models - Richard Schmieden

17:20 Towards quantitative precision for non-smooth interaction potentials in FRG flows - Franz Richard Sattler

17:20 The predictive power of asymptotic safety for an ALP model - Rafael Robson Lino dos Santos

17:20 SU(4) symmetry in Dirac materials - Application to twisted bilayer graphene - Nikolaos Parthenios

17:20 UV Conformal Window and Loss of Asymptotic Safety - Nahzaan Riyaz

17:20 Asymptotically safe Einstein-Palatini gravity - Abdol Sabor Salek

17:20 Background Effective Action with Nonlinear Massive Gauge Fixing - Dimitrios Gkiatas

17:20 mfRG analysis of the Attractive Hubbard Model - Aiman Al-Eryani

17:20 FRG analysis of the pseudogap opening in the 2D Hubbard model at finite doping - Hannes Braun

17:20 Holographic RG from Exact RG - Pavan Dharanipragada

17:20 Functional Renormalization for Multimatrix Models - Carlos I. Perez Sanchez

17:20 FRG based on the single boson exchange decomposition - Kilian Fraboulet

17:20 Incommensurate 2kF density wave quantum criticality - Lukas Debbeler

17:20 Spectral functions from renormalised flow equations - Jonas Wessely

17:20 EOS of QCD Matter - Andreas Geissel

17:20 Symmetry constraints for Callan-Symanzik flows in chiral models - Sebastian Töpfel

17:20 Universal scaling at a pre-thermal dark state - Tilman Enss

17:20 Multiloop functional renormalization group study of the Fermi polaron problem - Marcel Gievers

17:20 Entangled magnetic, charge, and superconducting pairing correlations in the 2-D Hubbard model - Sarah Heinzelmann

17:20 Truncated-unity FRG approach to minimal models of correlated moiré materials - ravn henkel

17:20 The F-theorem in the melonic limit - Davide Lettera

17:20 Real-time functional renormalization group for critical dynamics - Johannes Roth

17:20 Functional Spin RG for Rydberg Array Spin Hamiltonians - Benedikt Schneider

17:20 Asymptotic freedom and safety in quantum gravity - Saswato Sen

17:20 The $( 1 + 1 )$-dimensional Gross-Neveu model at non-zero $\mu$, $T$ and finite $N$ - Jonas Stoll

17:20 From KPZ to Inviscid Burgers universality : a FRG approach - Francesco Vercesi

17:20 Shift-symmetric Horndeski models in the asymptotically safe swampland? - Fabian Wagner

17:20 Fluctuation computation of gravitational RG flows on foliated spacetime - Jian Wang

17:20 The $( 1 + 1 )$-dimensional Gross-Neveu model at non-zero $\mu$, $T$ and finite $N$ - Niklas Zorbach

17:20 A study of a toy model of hydrodynamic turbulence using the NPRG - Côme Fontaine

17:20 Dilaton Quantum Gravity - Athanasios Kogios

17:20 Phonon renormalization and Pomeranchuk instability in the Holstein model - Max Oberon Hansen Niklas Cichutek
Tuesday 26 July 2022
09:00 Nevanlinna Analytical Continuation - Emanuel Gull
Nevanlinna Analytical Continuation
- Emanuel Gull
09:00 - 09:45
Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due to the bad conditioning of the continuation transform from imaginary to real frequencies, established methods tend to either wash out spectral features at high frequencies or produce spectral functions with unphysical negative parts. Here, we show that explicitly respecting the analytic `Nevanlinna' structure of the Green's function leads to intrinsically positive and normalized spectral functions, and we present a continued fraction expansion that yields all possible functions consistent with the analytic structure. Application to synthetic trial data shows that sharp, smooth, and multi-peak data is resolved accurately. Application to the band structure of silicon demonstrates that high energy features are resolved precisely. Continuations in a realistic correlated setup reveal additional features that were previously unresolved. By substantially increasing the resolution of real frequency calculations our work overcomes one of the main limitations of finite-temperature quantum simulations.
09:45 Towards a microscopic understanding of macroscopic properties of strong-interaction matter - Jens Braun
Towards a microscopic understanding of macroscopic properties of strong-interaction matter
- Jens Braun
09:45 - 10:30
10:30 Break
Break
10:30 - 11:00
11:00 The Spectral Geometry of de Sitter Space in Asymptotic Safety - Renata Ferrero
The Spectral Geometry of de Sitter Space in Asymptotic Safety
- Renata Ferrero
11:00 - 11:30
Within the functional renormalization group approach to Background Independent quantum gravity, we explore the scale dependent effective geometry of the de Sitter solution dS4. The investigation employs a novel approach whose essential ingredient is a modified spectral flow of the metric dependent d'Alembertian, or of similar hyperbolic kinetic operators. The corresponding one-parameter family of spectra and eigenfunctions encodes information about the nonperturbative backreaction of the dynamically gravitating vacuum fluctuations on the mean field geometry of the quantum spacetime. Used as a diagnostic tool, the power of the spectral flow method resides in its ability to identify the scale dependent subsets of field modes that supply the degrees of freedom which participate in the effective field theory description of the respective scale. A central result is that the ultraviolet of Quantum Einstein Gravity comprises far less effective degrees of freedom than predicted (incorrectly) by background dependent reasoning. Exploring the quantum spacetime's spatial geometry carried by physical fields, we find that 3-dimensional space disintegrates into a collection of coherent patches which individually can, but in their entirety cannot be described by one of the effective average actions occurring along the renormalization group trajectory.
11:30 Lorentzian quantum gravity and the graviton spectral function - Manuel Reichert
Lorentzian quantum gravity and the graviton spectral function
- Manuel Reichert
11:30 - 12:00
12:00 Functional Renormalization Group and 2PI Effective Action Formalism - Urko Reinosa
Functional Renormalization Group and 2PI Effective Action Formalism
- Urko Reinosa
12:00 - 12:30
12:30 Lunch break
Lunch break
12:30 - 14:30
14:30 Functional Flows for Complex Actions - Frederike Ihssen
Functional Flows for Complex Actions
- Frederike Ihssen
14:30 - 14:55
In my talk I will present a general functional renormalisation group framework for the computation of complex actions. Resolving the complex structure of quantum theories, such as QCD or condensed matter systems such as graphene or spin-imbalanced fermionic gases, may shed light on their phase structure. Restrictions on the phase structure come from exploring complex external fields such as a complex magnetic field in spin systems, or, more generally, complex couplings. The latter gives rise to Lee-Yang zeros in the complex (magnetisation) plane. For the explicit computations we consider both flows of the Wilsonian effective action and the 1PI effective action. In the present formulations the flow of the Wilsonian effective action has a general range of applicability and we obtain results for a $\phi^4$ theory in d=0,1,2,3,4 dimensions. These results are also compared with that for the 1PI effective action within its range of applicability. Computations are performed using the Discontinious Galerkin Methods. These advanced numerical methods enable us to solve these highly dynamic equations to very high proximity of the ensuing Lee-Yang singularities, and are reminiscent of reaction-diffusion equations (with an RG-kernel).
Quantum discontinuity fixed point and renormalization group flow of the SYK model - Peter Kopietz
Quantum discontinuity fixed point and renormalization group flow of the SYK model
- Peter Kopietz
14:30 - 14:55
We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. From a controlled truncation of the infinite hierarchy of the exact functional RG flow equations we identify several fixed points: Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of the transition in terms of a local effective Ising variable as is established for classical transitions. We propose an entangled quantum state at phase coexistence as a possible physical origin of this critical behavior.
14:55 Analysis of classical liquids using functional renormalization group - Takeru Yokota
Analysis of classical liquids using functional renormalization group
- Takeru Yokota
14:55 - 15:20
The development of theoretical methods for classical liquids is a longstanding problem in statistical mechanics. Accurate and efficient methods for classical liquids benefit, for instance, analysis of chemical reactions. In this talk, I will present an application of the functional renormalization group to classical liquids. We develop a formulation suitable for a hard-core repulsion and introduce the Kirkwood superposition approximation to truncate the hierarchy of the flow equations in the vertex expansion. In a numerical test on a one-dimensional solvable model, the functional renormalization group shows more accurate results than the integral-equation methods such as the hypernetted chain and the Percus-Yevick equation, which are conventional methods for classical liquids.
Pion-pion scattering from nucleon-meson fluctuations - Juergen Eser
Pion-pion scattering from nucleon-meson fluctuations
- Juergen Eser
14:55 - 15:20
I present calculations of the S-wave isospin-zero and isospin-two pion-pion scattering lengths within a nucleon-meson model with parity doubling. Both scattering lengths are computed in various approximations, ranging from a mean-field calculation towards the inclusion of loop corrections by means of the FRG. I thereby elucidate subtleties concerning the truncation of the effective action w.r.t. higher-derivative pion interactions. As the main result, simultaneous agreement for the isospin-zero and isospin-two scattering lengths with experimental data within the LPA'-truncation is found. The isoscalar sigma-mass is dynamically generated by the FRG integration, and is a prediction of the model. It ends being of the order of 500 MeV, i.e., much lower than the value (> 1 GeV) found in mean-field or one-loop treatment of this or related models. Finally, the convergence of the corresponding low-energy expansion of the quantum effective action in terms of pion momenta is discussed.
15:20 Asymptotic safety of Yang-Mills gauge theory in 5 dimensional spacetime - Masatoshi Yamada
Asymptotic safety of Yang-Mills gauge theory in 5 dimensional spacetime
- Masatoshi Yamada
15:20 - 15:45
The Yang-Mills gauge theory in 5 dimensional spacetime is perturbatively non-renormalizable, but could be asymptotically safe. We study the fixed point structure by using the functional renormalization group.
RG flows between Gaussian fixed points - Diego Buccio
RG flows between Gaussian fixed points
- Diego Buccio
15:20 - 15:45
A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form \phi\box^k\phi. We use the non-perturbative RG to study the flow from the free theory with four derivatives (k = 2) to the free theory with two derivatives (k = 1), in the presence of a shift-invariant interaction.
15:45 Break
Break
15:45 - 16:15
16:15 Multiloop flow equations for single-boson exchange fRG - Marcel Gievers
Multiloop flow equations for single-boson exchange fRG
- Marcel Gievers
16:15 - 16:35
The recently introduced single-boson exchange (SBE) decomposition [2] of the four-point vertex of interacting fermionic many-body systems is a conceptually and computationally appealing parametrization of the vertex. It relies on the notion of reducibility of vertex diagrams with respect to the bare interaction U, instead of a classification based on two-particle reducibility within the widely-used parquet decomposition. We re-derived the SBE decomposition in a generalized framework (suitable for extensions to, e.g., inhomogeneous systems or real-frequency treatments) following from the parquet equations. We then derived multiloop functional renormalization group (mfRG) flow equations [3] for the ingredients of this SBE decomposition, both in the parquet approximation, where the fully two-particle irreducible vertex is treated as an input, and in the more restrictive SBE approximation, where this role is taken by the fully U-irreducible vertex. Moreover, we give mfRG flow equations for the popular parametrization of the vertex in terms of asymptotic classes [4] of the two-particle reducible vertices. Since the parquet and SBE decompositions are closely related, their mfRG flow equations are very similar in structure. [1] E. Walter, M. Gievers, A. Ge, J. von Delft, F. B. Kugler, aXiv:2201.04878 (2022). [2] F. Krien, A. Valli, M. Capone, PRB 100, 155149 (2019). [3] F. B. Kugler, J. von Delft, Phys. Rev. Lett. 120, 057403 (2018). [4] N. Wentzell, G. Li, A. Tagliavini, C. Taranto, G. Rohringer, K. Held, A. Toschi, S. Andergassen PRB 102, 085106 (2020)
Timelike properties of QCD from functional methods - Jan Horak
Timelike properties of QCD from functional methods
- Jan Horak
16:15 - 16:35
We investigate timelike correlation functions in QCD via spectral functional renormalisation group and Dyson-Schwinger equations. Within the spectral formulation, direct access to the full complex structure of the theory is obtained. Studying the propagation of non-holomorphicities through the coupled system of DSEs in Yang-Mills theory, we obtain consistency conditions which constrain the analytic structure of possible solutions. We also present spectral functions in the Phi^4 theory from the spectral renormalization group. Finally, results for QCD transport coefficients are presented, obtained via closed diagrammatic representations in terms of timelike correlation functions.
16:35 Critical behaviour at thermal m-axial Lifshitz point and stability of the FFLO superfluid phases - Mateusz Homenda
Critical behaviour at thermal m-axial Lifshitz point and stability of the FFLO superfluid phases
- Mateusz Homenda
16:35 - 16:55
We apply nonperturbative renormalization group method to critical exponents of m-axial Lifshitz point as a function of dimensionality d, anisotropy m and the number of order parameter components N. Basing on the results we consider the stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in cold atom system.
Second order chiral phase transition in three flavor quantum chromodynamics? - Gergely Fejos
Second order chiral phase transition in three flavor quantum chromodynamics?
- Gergely Fejos
16:35 - 16:55
We calculate the renormalization group flows of all renormalizable interactions in the three dimensional Ginzburg--Landau potential for the chiral phase transition of three flavor quantum chromodynamics. On the contrary to the common belief we find a fixed point in the system that is able to describe a second order phase transition in the infrared. This shows that longstanding assumptions on the transition order might be false. If the transition is indeed of second order, our results can also be interpreted as indirect evidence that the axial anomaly restores at the transition temperature.
16:55 Lifetimes of the Fermi polaron and molecule at finite momentum from fRG - Jonas von Milczewski
Lifetimes of the Fermi polaron and molecule at finite momentum from fRG
- Jonas von Milczewski
16:55 - 17:15
We study theoretically the lifetimes of the attractive and the repulsive Fermi Polaron and the molecule at finite momentum in both two and three dimensions. To this end we developed a new technique that allows for the computation of Green's functions in the whole complex frequency plane using exact analytical continuation within the functional renormalization group. While conventional approaches like the NSCT method cannot determine these lifetimes, we are able to find the momentum dependent lifetime at different interaction strengths of both the attractive and repulsive polaron as well as the molecule. In our talk we discuss our findings and talk about possible experiments which could be conducted.
Spectral Functions in Banks-Zaks QCD - Yannick Kluth
Spectral Functions in Banks-Zaks QCD
- Yannick Kluth
16:55 - 17:15
The question of unitarity in perturbatively non-renormalisable field theories such as asymptotically safe quantum gravity is notoriously difficult to answer. A possible way to make progress lies in analysing spectral functions given by the Källén-Lehmann representation of the propagator. For spectral functions of scalar quantities, unitarity requires positive definiteness as well as normalisability. Such properties or even the existence of the Källén-Lehmann representation are however not clear for gauge fields or the graviton. To address these difficulties, we consider QCD in the Banks-Zaks phase which allows studying spectral functions of all elementary fields analytically using perturbative methods. In particular, this gives access to the propagator in the whole complex plane, which is difficult to achieve using conventional ERG methods. We analyse existence properties of spectral functions and test whether they fulfil positive definiteness and normalisability due to unitarity. Implications for spectral functions of conventional QCD or quantum gravity are discussed.
17:15 Active matter: A treasure trove of novel universality classes - Chiu Fan Lee
Active matter: A treasure trove of novel universality classes
- Chiu Fan Lee
17:15 - 17:35
A hallmark of living organisms is the ability to move around in their environments. In the fluid state, i.e., when the motile agents can exchange neighbours freely, the equations of motion that describes the system are called the Toner-Tu (TT) equations. The TT equations govern active fluids the same way that the Navier-Stokes equations govern simple fluids. Since the inception of the TT equations in 1995, dynamic renormalization group (DRG) analyses on the TT equations have led to the discovery of diverse novel nonequilibrium states of matter (or phases), and novel critical phenomena. In this talk, I will focus on the incompressible limit of the TT equations and elucidate the associated universal behaviour [1–5]. I will also discuss how exact RG may enable us to solve some key open questions in active matter physics. References: [1] Chen L, Lee C F, Maitra A and Toner J 2022 Packed swarms on dirt: two dimensional incompressible flocks with quenched and annealed disorder arXiv:2202.02865 [2] Chen L, Lee C F, Maitra A and Toner J 2022 Incompressible polar active fluids with quenched disorder in dimensions d > 2 arXiv:2203.01892 [3] Chen L, Lee C F and Toner J 2018 Incompressible polar active fluids in the moving phase in dimensions d > 2 New J. Phys. 20 113035 [4] Chen L, Lee C F and Toner J 2016 Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting Nat. Commun. 7 12215 [5] Chen L, Toner J and Lee C F 2015 Critical phenomenon of the order–disorder transition in incompressible active fluids New J. Phys. 17 042002
Functional renormalisation group for cosmic large-scale structure formation - Alaric Erschfeld
Functional renormalisation group for cosmic large-scale structure formation
- Alaric Erschfeld
17:15 - 17:35
The formation of cosmic large-scale structures can be described with a statistical field theory for the dynamics of dark matter. The functional renormalisation group is on the one hand studied using the underlying symmetries of the theory and in particular using an extended version of Galilean invariance. The corresponding generalised Ward identities allow to close and solve the flow equations for two-point correlation functions and relate to the so-called ‘sweeping effect’ known in fluid turbulence. On the other hand the flow equations are solved using an ansatz that corresponds to time-local effective dynamics for dark matter and can be understood as a vertex and derivative expansion of the effective action.
17:35 Cosmological constant problem and Hubble tension in scale-dependent cosmology - Cristóbal Laporte
Cosmological constant problem and Hubble tension in scale-dependent cosmology
- Cristóbal Laporte
17:35 - 17:55
In this work, a cosmological model based on the scale-dependent scenario of gravity is presented. We argue that the discrepancy between the Planck mass scale and the observed value of the cosmological constant can be largely attenuated if those quantities are understood as a result of effective, and thus scale-dependent, couplings. In the approach where the scale–dependence appears as a correction to the classical ΛCDM evolution, the potential to address the tensions between early and late time measurements of H0 is studied. Our results are compared to the renormalization group flow obtained within the asymptotic safety program, which reveals a stunning agreement. The work is based on JCAP 01 (2020) 021, JCAP 06 (2021) 019, and arXiv:2205.05592.
Novel critical phenomena in compressible polar active fluids - Patrick Jentsch
Novel critical phenomena in compressible polar active fluids
- Patrick Jentsch
17:35 - 17:55
Active matter describes the collective properties of particles that either possess internal energy or harness energy from the environment to actively self-propel. Diverse biological many-body systems, like tissue, or swarms of birds, fish or bacteria, are thus of this type, and many of which can be modelled as polar active fluids. Since these nonequilibrium systems break conservative laws that are intrinsic to thermal systems, such as energy and momentum conservation, diverse novel nonequilibrium phenomena are expected. In this talk, I will describe the use of the functional renormalization group to discover for the first time new universality classes in compressible polar active fluids that correspond to a multicritical point of these active systems. arXiv:2205.01610
17:55 Stability of the Yang-Mills theory vacuum and Cosmological Inflation. - George Savvidy
Stability of the Yang-Mills theory vacuum and Cosmological Inflation.
- George Savvidy
17:55 - 18:15
We examine the phenomena of the chromomagnetic gluon condensation in Yang-Mills theory and the problem of stability of the vacuum state. The stability of the vacuum state is analysed in the nonlinear regime. It is shown that an apparent instability of the Yang Mills vacuum is a result of quadratic approximation. In the case of (anti)self-dual fields the interaction of chromomagnetic modes of the quantised field in the direction of zero modes is calculated by using a new method of infrared regularisation as well as by the integration over the collective variables of self-interacting zero modes. The deformation of (anti)self-dual fields is also considered in the nonlinear regime by the integration, in this case, over the collective variables of self-interacting unstable modes. All these vacuum field configurations are stable and indicate that the vacuum is stable and is a superposition of many states. The deep interrelation between elementary particle physics and cosmology manifests itself when one considers the contribution of quantum fluctuations of vacuum fields to the dark energy and the effective cosmological constant. The contribution of zero-point energy exceeds by many orders of magnitude the observational cosmological upper bound on the energy density of the universe. Therefore it seems natural to expect that vacuum fluctuations of the fundamental fields would influence the cosmological evolution in any way. Our aim is to describe a recent investigation of the influence of the Yang-Mills vacuum polarisation and of the chromomagnetic condensation on the evolution of Friedmann cosmology, on inflation and on primordial gravitational waves.
Towards the phase structure of the complete Lorentzian Barrett-Crane model - Andreas Pithis
Towards the phase structure of the complete Lorentzian Barrett-Crane model
- Andreas Pithis
17:55 - 18:15
The Barrett-Crane spin foam and GFT model is a state-sum model which provides a quantization of first order Lorentzian Palatini gravity. Its complete formulation has only recently been accomplished. It is conjectured that the collective dynamics of the quanta of this model, which correspond to discrete building blocks of spacetime with spacelike, timelike and lightlike components, gives rise to continuum spacetime at criticality via phase transition. In this talk, we discuss how phase transitions for this and related models can be studied using Landau-Ginzburg mean-field theory. To this aim, we restrict the building blocks of the complete model such that the Feynman diagrams are dual to spacelike triangulations. We also include degrees of freedom which may be interpreted as discretized scalar fields on the lattice typically employed in quantum gravity to furnish a matter reference frame. This setting lays the groundwork to study the critical behavior when arbitrary Lorentzian building blocks are incorporated and represents a crucial advance to understand how phase transitions to continuum spacetime can be achieved in this setting. It also paves the way for the analysis of the phase structure of such models via functional renormalization group techniques in the future.
Wednesday 27 July 2022
09:00 Coarse graining to capture "relevant" information in biological systems - Stephanie Palmer
Coarse graining to capture "relevant" information in biological systems
- Stephanie Palmer
09:00 - 09:45
Biological systems must selectively encode partial information about the environment, as dictated by the capacity constraints at work in all living organisms. For example, we cannot see every feature of the light field that reaches our eyes; temporal resolution is limited by transmission noise and delays, and spatial resolution is limited by the finite number of photoreceptors and output cells in the retina. Classical efficient coding theory describes how sensory systems can maximize information transmission given such capacity constraints, but it treats all input features equally. Not all inputs are, however, of equal value to the organism. Our work quantifies whether and how the brain selectively encodes stimulus features, specifically predictive features, that are most useful for fast and effective movements. We have shown that efficient predictive computation starts at the earliest stages of the visual system, in the retina. We borrow techniques from statistical physics and information theory to assess how we get terrific, predictive vision from these imperfect (lagged and noisy) component parts. In broader terms, we aim to build a more complete theory of efficient encoding in the brain, and along the way have found some intriguing connections between formal notions of coarse graining in biology and physics.
09:45 Large Deviations in the Climate System: Extreme Events and Metastability - Valerio Lucarini
Large Deviations in the Climate System: Extreme Events and Metastability
- Valerio Lucarini
09:45 - 10:30
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of great urgency, especially given the ongoing climate change and the evolving climate crisis. In statistical physics, complex, many-particle systems are studied successfully using the Large Deviation Theory (LDT). In the spirit of Hasselmann's programme, a great potential exists for applying LDT to problems relevant for climate science. In particular, LDT allows for understanding the fundamental properties of persistent deviations of climatic fields from the long-term averages and for associating them to low-frequency, large scale patterns of variability. This allows one to introduce a notion of typicality with regard to extreme events. These applications are of key importance to improve our understanding of high-impact weather and climate events. We will present several applications to the case of recent heatwaves (2010 Russian Heatwave, 2021 Western North America Heatwave) and cold spells (2010 Mongolian Dzud, 2019 Canadian Cold Spell). Furthermore, taking advantage of the formalism of Graham's quasipotential, LDT provides powerful tools for evaluating the probability of noise-induced transitions between competing metastable states of the climate system and for understanding the multiscale, hierarchical properties of the so-called dynamical landscape. We will show how this framework can be used to better understand the - arguably - most important critical transition of the Earth system, associated with the dichotomy between Snowball and Warm climate. The final transition to the Warm state that occurred about 600 Mya has been key for the eventual emergence of multicellular life in our planet. References: V.M. Galfi, V. Lucarini, Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory, Phys. Rev. Lett. 127, 058701 (2021) V.M. Galfi, V. Lucarini, F. Ragone, J. Wouters, Applications of Large Deviation Theory in Climate Science and Geophysical Fluid Dynamics, Riv. Nuovo Cimento 44, 291–363 (2021) G. Margazoglou, T. Grafke, A. Laio, V. Lucarini, Dynamical Landscape and Multistability of the Earth's Climate, Proc. R. Soc. A 477, 2021001920210019 V. Lucarini, T. Bodai, Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions, Nonlinearity 33, R59 (2020) V. Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)
10:30 Break
Break
10:30 - 11:00
11:00 Essential Renormalisation Group - Kevin Falls
Essential Renormalisation Group
- Kevin Falls
11:00 - 11:30
11:30 Vanishing regulators - Luca Zambelli
Vanishing regulators
- Luca Zambelli
11:30 - 12:00
12:00 Glory and misery of the Derivative Expansion: Ten years later - Nicolás Wschebor
Glory and misery of the Derivative Expansion: Ten years later
- Nicolás Wschebor
12:00 - 12:30
12:30 Lunch break
Lunch break
12:30 - 14:30

14:30 Wednesday
Wednesday
14:30 - 15:45

15:45 Break
Break
15:45 - 16:15
16:15 Coupling fermions to unimodular gravity - Reinhard Alkofer
Coupling fermions to unimodular gravity
- Reinhard Alkofer
16:15 - 16:35
Sextic tensor field theories - Sabine Harribey
Sextic tensor field theories
- Sabine Harribey
16:15 - 16:35
Tensor models admit a melonic large N limit. In d dimensions, they give rise to a new family of conformal field theories. Such melonic CFTs were studied for tensor models in rank 3 with quartic interactions. However, a non-trivial infrared fixed point with a real spectrum of conformal dimensions was only found for a model with a long-range propagator and a purely imaginary coupling constant. We wish to understand how this depends on the rank of the tensors and on the order of the interactions. I will present here the renormalization group flow of two tensor models with sextic interactions in rank 3 and 5 with either short or long-range propagators. In rank 3, we found non-trivial IR fixed points for both the short-range and the long-range models, with precursors at next-to-leading order in short range. We also found a real spectrum of bilinear operators in both cases. Surprisingly, in rank 5, we only found a non-interacting fixed point.
16:35 Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories - Junichi Haruna
Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
- Junichi Haruna
16:35 - 16:55
Gradient Flow Exact Renormalization Group (GFERG) is a framework to define the Wilson action via a gradient flow equation proposed by Ref.[1]. Because it preserves gauge symmetries obviously, it is a promising approach to study non-perturbative aspects of gauge theories or quantum gravity. On the other hand, some scalar models (such as the CP^N-1 model or the O(N) non-linear sigma model) share similar properties with these theories and have been investigated as their toy models. In this talk, we study the fixed point structure of the GFERG equation associated with a general gradient flow equation for scalar field theories. We show that the fixed point structure is the same as that of the conventional Wilson-Polchinski (WP) equation in general. Furthermore, we discuss that the GFERG equation has a similar RG flow structure around a fixed point to the WP equation. We illustrate these results with the O(N) non-linear sigma model in 4-epsilon dimensions and the Wilson-Fisher fixed point. This talk is based on Ref. [2]. [1] H. Sonoda and H. Suzuki, PTEP2021 No.2, (2021) 023B05 [arXiv:2012.03568 [hep-th]] [2] Y.Abe, Y.Hamada and J.Haruna, [arXiv:2201.04111 [hep-th]]
The weak-gravity bound in asymptotically safe gauge-gravity systems - Marc Schiffer
The weak-gravity bound in asymptotically safe gauge-gravity systems
- Marc Schiffer
16:35 - 16:55
In this talk I will discuss the weak-gravity bound, which has been discovered in asymptotically safe gravity-matter systems. It limits the maximum strength of the gravitational fluctuations. Specifically, I will discuss the weak-gravity bound in gauge-gravity systems with more than one gauge field, to discover whether systems with 12 gauge fields (like the Standard Model) exhibit such a bound and whether the gravitational fixed point evades it. Furthermore, I will highlight that the existence of the weak-gravity bound in gauge-gravity systems also has important phenomenological consequences: it is key to a proposed mechanism that bounds the spacetime dimensionality from above to four or five dimensions. I will discuss strengthened evidence for this mechanism, which indicates that the predictive power of the asymptotic safety paradigm could extend to parameters of the spacetime geometry. Finally, I will present first steps towards investigating the weak-gravity bound beyond polynomial truncations.
16:55 Nonvanishing gravitational contribution to matter beta functions for vanishing regulators - Gustavo de Brito
Nonvanishing gravitational contribution to matter beta functions for vanishing regulators
- Gustavo de Brito
16:55 - 17:15
In this talk, I will explore the effect of quantum gravity on matter couplings within a Renormalization Group framework. In particular, I will focus on results obtained from a class of interpolating regulators that allow us to extract certain universal pieces from non-universal quantities. I will discuss an explicit example of how misleading conclusions can be drawn by analyzing the gravitational contributions to beta functions instead of analyzing universal quantities, such as critical exponents, that can be extracted from the beta functions. This could be key to explaining the differences between perturbative studies and Functional Renormalization Group studies.
Operator product expansion coefficients from the nonperturbative functional renormalization group - Félix Rose
Operator product expansion coefficients from the nonperturbative functional renormalization group
- Félix Rose
16:55 - 17:15
Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient c112 associated with the operators O1∼φ and O2∼φ2 in the three-dimensional O(N) universality class and in the Ising universality class (N=1) in dimensions 2≤d≤4. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of d and N considered.
17:15 Interacting fixed points of fermionic field theories - Charlie Cresswell-Hogg
Interacting fixed points of fermionic field theories
- Charlie Cresswell-Hogg
17:15 - 17:35
Using functional RG for fermions, we study new fixed points of 3d Gross-Neveu theories beyond chiral symmetry. At large N we find that the sextic coupling becomes exactly marginal, leading to a line of UV fixed points. We discuss the generation of mass in these theories, the phase diagram and the Bardeen-Moshe-Bander phenomenon for fermions. Similarities with critical scalar theories are highlighted. We also discuss aspects of four-fermion interactions in four dimensions.
Running Newton Coupling, Scale Identification and Black Hole Thermodynamics - Nobuyoshi Ohta
Running Newton Coupling, Scale Identification and Black Hole Thermodynamics
- Nobuyoshi Ohta
17:15 - 17:35
We discuss the quantum improvement of black hole solutions in the context of asymptotic safety. The Newton coupling in this formulation depends on an energy scale, which must be identified with some length scale in order to study physical consequences to black holes. However, no physical principle has so far been known for the identification. Here we propose that the consistency of the first law of thermodynamics is the principle that should determine physically sensible scale identification, at least close to the horizon. We show that this leads to a natural solution that the Newton coupling should be a function of the horizon area and find a universal formula for the quantum entropy, which agrees with the standard Bekenstein-Hawking entropy for constant Newton coupling, for Kerr black holes and other higher-dimensional black holes. This suggests that the Newton coupling is a function of the area at fixed radius near the horizon, and also away to infinity, where the quantum effects may not be so important.
17:35 Formation and evaporation of quantum black holes from the decoupling mechanism - Johanna Borissova
Formation and evaporation of quantum black holes from the decoupling mechanism
- Johanna Borissova
17:35 - 17:55
Quantum counterparts to classical black holes provide an exciting ground for phenomenology of quantum gravity. Within the functional renormalization group approach to quantum gravity, we propose a novel method to account for quantum effects in classical spacetimes. At the core of our construction is the decoupling mechanism: when a physical infrared scale overcomes the effect of the artificial regulator implementing the Wilsonian integration of fluctuating modes, the effective average action freezes out and approximates the standard quantum effective action. Starting from the Einstein-Hilbert truncation, we use the decoupling mechanism to explore the dynamics of quantum black holes in the phases of collapse and evaporation.
Gross-Neveu SO(3) criticality in spin-orbital liquids: FRG vs higher-order perturbation theory - Shouryya Ray
Gross-Neveu SO(3) criticality in spin-orbital liquids: FRG vs higher-order perturbation theory
- Shouryya Ray
17:35 - 17:55
The Gross-Neveu SO(3) universality class in three spacetime dimensions describes a quantum critical point between a Dirac semimetal and a long-range-ordered phase in which the fermion spectrum is only partially gapped out. Such a quantum critical point has recently been predicted to be realizable in two-dimensional spin-orbital magnets with strong exchange frustration. Here, I shall report on our efforts to characterize the quantum critical behaviour of the Gross-Neveu-SO(3) universality class using the functional renormalization group in the improved local potential approximation, and compare with our three-loop and second-order large-N results. Time permitting, I shall also discuss some of the qualitative behaviour for general spactime dimension and flavour number, which shows some distinctive features that are absent in the corresponding Gross-Neveu-Ising and -Heisenberg incarnations.
17:55 --
--
17:55 - 18:15
Gauge dependence of Essential Quantum Einstein Gravity - Oleg Melichev
Gauge dependence of Essential Quantum Einstein Gravity
- Oleg Melichev
17:55 - 18:15
The Essential Functional Renormalisation Group, applied to quantum gravity, allows the metric to be reparametrised along the RG trajectory, such that only the essential couplings are renormalised. This allows to simplify the study of the properties of the fixed points. It is of interest to investigate the behaviour of the solutions with respect to a change of the gauge fixing parameters. In this work we compute the flow up to the fourth order in derivative expansion using a generic class of gauges for which the kinetic operator becomes nonminimal. To this end we implement the off-diagonal heat kernel technique also known as the Universal RG Machine. We compute the position of the fixed points using Landau and Feynman gauges and discuss the applicability of used approximations.
18:30 BBQ
BBQ
18:30 - 21:30
Thursday 28 July 2022
09:00 Operator Product Expansion - Stefan Hollands
Operator Product Expansion
- Stefan Hollands
09:00 - 09:45
With the help of the renormalization group flow equations a la Wilson-Wegner-Polchinski-Wetterich several hitherto conjectural properties and several new properties of the operator product expansion (OPE) have been established in recent times such as 1) its convergence properties 2) its algebraic properties ("associativity"), or 3) a functional master equation for the OPE coefficients. With the help of the master equation, a differential equation for the flow of the conformal data (OPE coefficients and anomalous dimensions) in $d$-dimensional CFTs under a marginal perturbation can be established. In this talk, I give an overview over such results.
09:45 Unconventional superconductivity in moiré transition metal dichalcogenides - Laura Classen
Unconventional superconductivity in moiré transition metal dichalcogenides
- Laura Classen
09:45 - 10:30
10:30 Break
Break
10:30 - 11:00
11:00 The O(N) models in the vicinity of d=2 - Pawel Jakubczyk
The O(N) models in the vicinity of d=2
- Pawel Jakubczyk
11:00 - 11:30
11:30 Non-equilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions - Dante Kennes
Non-equilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions
- Dante Kennes
11:30 - 12:00
12:00 Structure functions in shell models of turbulence - Léonie Canet
Structure functions in shell models of turbulence
- Léonie Canet
12:00 - 12:30
Shell models are simplified models of turbulence, describing discrete Fourier modes of velocity coupled via purely local interactions in spectral space. Yet these simple models reproduce all characteristic features of Navier-Stokes turbulence, including intermittency. I will present a FRG analysis of these models, and show that the turbulent regime corresponds to a non-trivial fixed-point. I will explain its specific properties and present the results for the structure functions.
12:30 Lunch break
Lunch break
12:30 - 14:30
14:30 A Generalized fRG Solver for Material Systems - David Campbell
A Generalized fRG Solver for Material Systems
- David Campbell
14:30 - 14:55
We summarize recent work with Nahom YIrga on the development of a generalized functional Renormalization Group (fRG) approach to condensed matter systems. Our approach combines momentum decoupling (as in standard RG calculations) with frequency decoupling (as in the dynamical mean field theories) and band decoupling (necessary to study the multiband models that apply to various high temperature superconductors and related materials). Importantly, we are able to include both electron-electron interactions and electron-phonon interactions in our solver. We give examples of applications of two- and three-band models for the Cuprate superconductors and of the effects of both Holstein and Su-Schrieffer-Heeger phonons on the phase diagrams of two-dimensional Hubbard models of strongly correlated systems.
Non perturbative strings, asymptotic safety, and the swampland - Alessia Platania
Non perturbative strings, asymptotic safety, and the swampland
- Alessia Platania
14:30 - 14:55
14:55 Clock models from second order of the derivarive expansion of the functional renormalization group - Carlos Sánchez
Clock models from second order of the derivarive expansion of the functional renormalization group
- Carlos Sánchez
14:55 - 15:20
Universal quantities at high orders of the derivative expansion - Gonzalo De Polsi
Universal quantities at high orders of the derivative expansion
- Gonzalo De Polsi
14:55 - 15:20
In the context of the Functional Renormalization Group, the Derivative Expansion is one of the most employed approximation schemes. In the last decade, this scheme has been pushed up to order $\mathcal{O}(\partial^6)$ for the Ising model universality class and to order $\mathcal{O}(\partial^4)$ for the $O(N)$ models. This allowed us to comprehend better the properties and behaviour of this scheme and enabled the introduction of error bars for the computed quantities. As a consequence, in the last few years not only critical exponents but also universal amplitude ratios were computed with a precision and accuracy comparable with the most precise results in the literature and, in some cases, they are the reference results. In this talk I will discuss these recent results in view of the new developments of the derivative expansion.
15:20 Fluid dynamic aspects of the exact renormalization group - Adrian Koenigstein
Fluid dynamic aspects of the exact renormalization group
- Adrian Koenigstein
15:20 - 15:45
The lower critical dimension of phi4 theory from Functional RG - Lucija Nora Farkas
The lower critical dimension of phi4 theory from Functional RG
- Lucija Nora Farkas
15:20 - 15:45
The lower critical dimension $d_l$ is the spatial dimension on which fluctuations destroy the phase transition. In the scalar phi4 theory, this happens due to the proliferation of kinks. This differs for example from the O(N) case where it is a result of Goldstone modes and where $d_l=2$ is well understood in the RG formalism. We explore whether the Functional Renormalization Group methods can be used to capture those localized excitations and investigate the phase transition just above the lower critical dimension. We have studied the fixed point solutions and discovered that the effective potential develops a boundary layer near its minimum as one approaches the $d_l$ limit, a feature that was not identified in previous works. We explain how the boundary layer determines the critical behavior in the vicinity of the lower critical dimension.
15:45 Break
Break
15:45 - 16:15
16:15 Constructing CFTs from AdS flows - Markus Fröb
Constructing CFTs from AdS flows
- Markus Fröb
16:15 - 16:35
Employing the RG flow equations for weakly coupled quantum field theories in AdS, I show how one can apply the AdS/CFT correspondence to obtain flow equations for the dual CFTs. In this duality, loop corrections in the AdS bulk are mapped to 1/N corrections in the CFT. I derive recursion relations for CFT correlation functions which generalize existing results in the large-N limit to all orders in the 1/N expansion, and show how these translate directly into recursion relations for the corresponding Mellin amplitudes.
Spins, pseudo-Majoranas and the functional RG - Björn Sbierski
Spins, pseudo-Majoranas and the functional RG
- Björn Sbierski
16:15 - 16:35
Frustrated three-dimensional quantum magnets bear a rich phenomenology but are notoriously hard to treat theoretically. We show how a SO(3) Majorana representation of spin operators, in combination with the functional renormalization group allows for quantitative simulations at finite temperatures. Focusing on Heisenberg magnets, we establish a finite-size scaling approach and extract critical temperatures and -exponents. For the Pyrochlore lattice, we discuss the improvements introduced by two-loop contributions in the flow equations. We also show how the method can be applied so meet some challenges of long-range interacting spin Hamiltonians arising in the context of Rydberg atom array quantum simulators.
16:35 A Rigorous Treatment of the Wetterich Equation - Jobst Ziebell
A Rigorous Treatment of the Wetterich Equation
- Jobst Ziebell
16:35 - 16:55
Spin functional renormalization group for dimerized quantum spin systems - Andreas Rückriegel
Spin functional renormalization group for dimerized quantum spin systems
- Andreas Rückriegel
16:35 - 16:55
We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean field critical exponents at the two quantum critical points.
16:55 The low-temperature phase of the O(N) models below two dimensions - Andrzej Chlebicki
The low-temperature phase of the O(N) models below two dimensions
- Andrzej Chlebicki
16:55 - 17:15
We investigate the low-temperature behaviour of the O(N) models for 1<d,N<2. We identify a phase with algebraic correlations similar to the Kosterlitz-Thouless phase but characterized by a universal anomalous dimension. We sketch the region of the (d,N)-plane where the algebraic low-temperature phase is present and calculate the anomalous dimension as a function of (d,N).
Ultraviolet properties of Lifshitz-type field theories - Dario Zappala
Ultraviolet properties of Lifshitz-type field theories
- Dario Zappala
16:55 - 17:15
We analyse some aspects of higher derivative Lifshitz-type field theories that exhibit anisotropic scaling laws near the Lifshitz fixed point, with explicit breaking of Lorentz symmetry. Specifically, anisotropic models in 3+1 dimension with dynamical exponent z=3 and with all momentum dependent vertex operators discarded, show restoration of Lorentz symmetry in the infrared region. At the same time, ultraviolet divergences are strongly smoothened and, in particular, models with Liouville-like potential show asymptotic freedom. Generalisation of this picture, that includes fermionic and gauge degrees of freedom, is discussed.
17:15 Asymptotically safe scalar-tensor theories - Antonio Pereira
Asymptotically safe scalar-tensor theories
- Antonio Pereira
17:15 - 17:35
Tetracriticality in O(N) models - Shunsuke Yabunaka
Tetracriticality in O(N) models
- Shunsuke Yabunaka
17:15 - 17:35
We study the tetracritical fixed point in O(N) models with NPRG. Increasing N, we find that the tetracritical FP continues to exist up to N=\infty, which is a different scenario from what we found for the tricritical FP. The FP approaches the WF FP except at a field value. We actually find that higher derivatives of the FP potential at the special point becomes singular in a way that the FP cannot be found with conventional large N analysis.
17:35 Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants - Maximilian Becker
Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants
- Maximilian Becker
17:35 - 17:55
Benchmarking effective actions and their flow equations in zero dimensions - Peter Millington
Benchmarking effective actions and their flow equations in zero dimensions
- Peter Millington
17:35 - 17:55
We can define various quantum effective actions, each of which may have particular utility or convenience, in analogy to the Routhians of classical mechanics. In this talk, we provide an update on efforts to provide pedagogical and explicit illustrations of the construction and subtleties of various effective actions and, in particular, the one-particle-irreducible, average one-particle-irreducible and two-particle-irreducible effective actions. By focussing on zero-dimensional “QFTs”, we are able to make concrete one-to-one comparisons in terms of analytic expressions for the effective actions, and the relevant n-point functions and sources, and to benchmark various approaches to the derivation of exact flow equations.
Friday 29 July 2022
09:00 From holographic RG to information flows - Johanna Erdmenger
From holographic RG to information flows
- Johanna Erdmenger
09:00 - 09:45
I will give a brief overview of the holographic RG in the context of the AdS/CFT correspondence, considering both flows to IR fixed points as well as to confining dual field theories. I will highlight recent developments on relating information-theory concepts such as entanglement entropy to geometric objects in dual hyperbolic spaces. Moreover, I will present recent results on the analogy between the RG and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by explicitly computing the relative entropy or Kullback-Leibler divergence in both the one- and two-dimensional Ising models under decimation RG, as well as in a feedforward neural network as a function of depth. We observe qualitatively identical behavior characterized by the monotonic increase to a parameter-dependent asymptotic value.
09:45 Functional renormalization for the beginning and the present Universe - Christof Wetterich
Functional renormalization for the beginning and the present Universe
- Christof Wetterich
09:45 - 10:30
Functional renormalization for quantum gravity with a scalar field computes at the fixed point the scaling solution for the effective scalar potential for the whole range of the scalar field. Similarly, one investigates the scaling solution for the scalar-field-dependent effective Planck mass ( coefficient function of the curvature scalar). The solution of the field equations derived from the corresponding effective action determines the cosmology. The region of small scalar field values leads to an inflationary cosmology at the beginning of the Universe. The large field region describes dynamical dark energy in the present Universe, with a cosmological constant that vanishes in the infinite future. Between the two limits the field-dependent couplings of the scaling solution account for the running couplings in the scale invariant standard model of particle physics. No flow away from the scaling solution may be needed.
10:30 Break
Break
10:30 - 11:00
11:00 Computational fluid dynamics and the fRG - Nicolas Wink
Computational fluid dynamics and the fRG
- Nicolas Wink
11:00 - 11:30
The talk reviews the application of computational fluid dynamics techniques to flow equations, explored in a recent series of paper. Hereby, a detailed explanation of the deep connection between RG flows and convection-diffusion equations is given. These properties, as well as the connection to phase transitions, are made explicit at the example of O(N) theories in various variations. Finally, the extension beyond such simple models and truncations of the effective action will be discussed.
11:30 Luttinger Liquids at the Edge of Quantum Hall Systems - Marcello Porta
Luttinger Liquids at the Edge of Quantum Hall Systems
- Marcello Porta
11:30 - 12:00
We consider the edge transport properties of a generic class of interacting quantum Hall systems on a cylinder, in the infinite volume and zero temperature limit. We prove that the large-scale behavior of the edge correlation functions is effectively described by the multi-channel Luttinger model. In particular, we prove that the edge conductance is universal, and equal to the sum of the chiralities of the non-interacting edge modes. The proof is based on rigorous renormalization group methods, that allow to fully take into account the effect of backscattering at the edge. Universality arises as a consequence of the vanishing of the beta function for the emergent multi-channel Luttinger liquid, combined with lattice Ward identities for the microscopic 2d theory and with the non-renormalization of the chiral anomaly for the emergent QFT. Joint work with Vieri Mastropietro.
12:00 A functional RG perspective on the 2D Hubbard model - Sabine Andergassen
A functional RG perspective on the 2D Hubbard model
- Sabine Andergassen
12:00 - 12:45
The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics. Despite its simplicity, the model exhibits a rich physical behavior and has been proposed as an effective model for electrons moving in the copper-oxygen planes of cuprate high-temperature superconductors. The functional RG stability analysis, originally developed for the 2D Hubbard model describing tight-binding fermions with a local interaction on a square lattice, provided the first conclusive evidence for the existence of d-wave superconductivity with a sizable energy gap at moderate interaction strength. Since then large progress has been achieved in its treatment with various theoretical and numerical methods. We here present recent advancements in the functional RG showing that the flow can be brought to a quantitative level for two-dimensional problems, which opens the route towards the realistic numerical investigations of more general systems.
12:45 Lunch break
Lunch break
12:45 - 14:00

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