On finite symmetries and their gauging in two dimensions

Abstract

It is well-known that if we gauge a ${\mathbb{Z}}_n$ symmetry in two dimensions, a dual ${\mathbb{Z}}_n$ symmetry appears, such that re-gauging this dual ${\mathbb{Z}}_n$ 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.

73 pages, v2: correct treatment of pivotal structure leading to the resolution of a contradiction between non-trivial anomaly and unitarity

References in corpus (5)

• Generalized Global Symmetries
• Theta, Time Reversal, and Temperature
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups
• Discrete torsion defects

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