# From orbifolding conformal field theories to gauging topological phases

## TL;DR

This paper explores how gauging symmetries in topological phases of matter can be understood through orbifold constructions on their edge conformal field theories, predicting properties of resulting anyonic excitations.

## Contribution

It introduces a method to analyze gauging of symmetries in topological phases via orbifold CFT techniques, linking bulk properties to boundary conformal theories.

## Key findings

- Predicts fusion, spin, braiding of anyons after gauging
- Applies method to $ ext{Z}_N$, $SU(3)_1$, and $SO(8)_1$ theories
- Connects bulk gauging procedures with boundary orbifold CFTs

## Abstract

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1) dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function, and predicts the fusion, spin and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual $\mathbb{Z}_N$ gauge theory, the twofold symmetric $SU(3)_1$, and the $S_3$-symmetric $SO(8)_1$ Wess-Zumino-Witten theories.