Theory of twist liquids: Gauging an anyonic symmetry

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 Z₂-symmetric toric code, SO(2N)₁ and SU(3)₁ state as well as the S₃-symmetric SO(8)₁ state and a non-Abelian chiral state we call the "4-Potts" state.