Modular operator, correlation functions and symmetry resolution

by Henri Scheppach (University of Würzburg)

Thursday 28 May 2026, 14:15 → 15:30 Europe/Berlin

Abbeanum/1-HS2 - Straubel-HS (TPI, FSU Jena)

We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of finite-dimensional algebras with fixed subregion charge values. An important ingredient is the combination of these algebras using direct integrals. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functions for hyperfinite algebras. Our approach establishes a mathematical foundation for recent results on symmetry resolution and modular theory in conformal field theory. Our analysis applies both to charges defined on a continuous range, or on a discrete set. The latter is of interest for condensed matter theory.