On finite symmetries and their gauging in two dimensions

By Lakshya Bhardwaj, Yuji Tachikawa. 2017

310 citations recorded by the source corpus.

A bstractIt 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.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a23af4c34ee2838e1a4e8fdc61ae1e03b8a1fbb

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Citations in the corpus

Universal Non‐Invertible Symmetries (2022, unknown): “We refer the readers to the textbook [27] for a more careful exposition and [37, 38] for physicists-friendly reviews.”
Generalized Symmetries in Condensed Matter (2022, unknown): “Categorical symmetries have been studied most extensively in 1+1d QFTs ( e.g. (104, 96, 100, 105, 106, 101, 107, 108, 109)), where they can be used constrain RG flows.”
On 2-group global symmetries and their anomalies (2018, unknown): “Recent investigations include [2, 3].”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, result): “Building on earlier work of [2–7], it has been advocated that non-invertible topological defects should be viewed as generalizations of ordinary global symmetries [8, 9].”
Higher Gauging and Non-invertible Condensation Defects (2022, background): “This has been discussed extensively for non-invertible 0-form symmetries in 1+1d [35,39,40,3,15,14,41] and for non-invertible 1-form symmetries in 2+1d (see [42–45] for recent discussions).”
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “abelian magnetic symmetries may be found in [4].”