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arXiv · 1510.03475

On Gauging Symmetry of Modular Categories

Shawn X. Cui·César Galindo·Julia Yael Plavnik·Zhenghan Wang
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Abstract

Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group $G$, gauging is a 2-step process: first extend the UMC to a $G$-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the $H^4$-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.

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Shawn X. Cui, César Galindo, Julia Yael Plavnik, Zhenghan Wang. 2016-02-23. On Gauging Symmetry of Modular Categories. https://doi.org/10.1007/s00220-016-2633-8

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