’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology

Lukas Müller, Richard J. Szabo

Research output: Contribution to journalArticle

Abstract

We study discrete symmetries of Dijkgraaf–Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such a symmetry to admit ’t Hooft anomalies in terms of the Lyndon–Hochschild–Serre spectral sequence. We give an explicit realization of a discrete gauge theory with ’t Hooft anomaly as a state on the boundary of a higher-dimensional Dijkgraaf–Witten theory. This allows us to calculate the 2-cocycle twisting the projective representation of physical symmetries via transgression. We present a general discussion of the bulk-boundary correspondence at the level of partition functions and state spaces, which we make explicit for discrete gauge theories.
Original languageEnglish
Pages (from-to)1-47
Number of pages47
JournalCommunications in Mathematical Physics
Early online date9 Aug 2019
DOIs
Publication statusE-pub ahead of print - 9 Aug 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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