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On finite symmetries and their gauging in two dimensions

  • Lakshya Bhardwaj
  • Yuji Tachikawa
Open Access
Regular Article - Theoretical Physics

Abstract

It is well-known that if we gauge a ℤn symmetry in two dimensions, a dual ℤn symmetry appears, such that re-gauging this dual ℤn 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.

Keywords

Anyons Discrete Symmetries Global Symmetries Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan

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