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arXiv · 1811.05446

't Hooft anomalies of discrete gauge theories and non-abelian group cohomology

Lukas Müller·Richard J. Szabo
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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.

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BibTeXRIS

Lukas Müller, Richard J. Szabo. 2018-11-13. 't Hooft anomalies of discrete gauge theories and non-abelian group cohomology. https://doi.org/10.1007/s00220-019-03546-w

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