Crossed product algebras and generalized entropy for (arbitrary) subregions

by Ro Jefferson (Utrecht University)

Wednesday 31 Jan 2024, 14:30 → 15:30 Europe/Rome

Room 281 (Physics and astronomy department)

Abstract: An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II factor, in which traces and hence von Neumann entropy can be well-defined. In this talk, I will generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, paving the way to the study of entanglement entropy without UVUV  divergences. If time permits, I will discuss the application of this construction in both flat space and AdS/CFT. In the latter case, the algebraic perspective also provides a simple argument for why the bulk dual of a boundary subregion must be the entanglement wedge.