Renormalisable four-fermion interactions in four dimensions

by Charlie Cresswell-Hogg (U. Sussex)

Thursday 25 Jun 2026, 14:15 → 15:45 Europe/Berlin

Four-fermion interactions are important in many areas of particle physics, from effective descriptions of weak interactions and QCD to parametrisations of new physics in frameworks such as SMEFT. In this talk I demonstrate that four-fermion interactions may develop strongly coupled UV fixed points in four dimensional QFTs. Contrary to weakly coupled expectations, their high energy limit may be (near-) conformal, with radically altered scaling behaviour due to large anomalous dimensions. The idea will be illustrated in a purely fermionic model of the Gross-Neveu type using the toolbox of the large-N expansion. I will show that the model, suitably extended with higher-derivative and eight-fermion interactions, is renormalisable to all orders in the expansion, with physical predictions being fully determined in terms of three parameters, and discuss RG running and operator scaling dimensions in the near-conformal UV regime. I will also discuss implications for effective field theory and the wider landscape of fermionic QFTs.