Twist liquids and gauging anyonic symmetries

Topological phases of matter in $(2+1)$D are frequently equipped with global symmetries that relabel anyons without changing the fusion and braiding structures. Twist defects are static symmetry fluxes that permute the labels of orbiting anyons. {\em Gauging} or {\em melting} these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases known as {\em twist liquids}. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. Generalizing a discrete gauge theory, we represent the anyons in a twist liquid by compositions of not only fluxes and charges but also quasiparticle supersectors. We show the gauging transition amplifies the total quantum dimension by $|G|$, the order of the symmetry group, and thus modifies the topological entanglement entropy.