Theory of Twist Liquids: Gauging an Anyonic Symmetry

Abstract

Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the ${\mathbb{Z}}_2$-symmetric toric code, $SO(2N{)}_1$ and $SU(3{)}_1$ state as well as the $S_3$-symmetric $SO(8{)}_1$ state and a non-Abelian chiral state we call the "4-Potts" state.

69 pages, 16 figures

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