On finite symmetries and their gauging in two dimensions

2017/04/07 by Lakshya Bhardwaj, Yuji Tachikawa · 1 voice · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.CT

paper · pdf · doi:10.1007/jhep03(2018)189

arxiv published 2017/04/07 · arxiv updated 2017/10/26

Abstract

It is well-known that if we gauge a ℤ_n symmetry in two dimensions, a dual ℤ_n symmetry appears, such that re-gauging this dual ℤ_n symmetry leads back to the original theory. We describe how this can be generalized to non-Abelian groups, by enlarging the concept of symmetries from those defined by groups to those defined by unitary fusion categories. We will see that this generalization is also useful when studying what happens when a non-anomalous subgroup of an anomalous finite group is gauged: for example, the gauged theory can have non-Abelian group symmetry even when the original symmetry is an Abelian group. We then discuss the axiomatization of two-dimensional topological quantum field theories whose symmetry is given by a category. We see explicitly that the gauged version is a topological quantum field theory with a new symmetry given by a dual category.

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Discussions

• I am trying to understand some of the introductory statements in this paper , as well as some other comments I have read in the literature about gauging finite symmetries. First, I want to understand [stackexchange, 2 points]