Note on proliferation transitions of non-Abelian anyons

Abstract

We study phase transitions out of a (2+1)d topological phase driven by the proliferation of anyons in a braided fusion subcategory. We describe a general theoretical framework for such transitions, in which the topological quantum field theory (TQFT) is coupled to dynamical matter associated with anyons in the subcategory. We interpret this construction using symmetry topological field theory (SymTFT), where the dynamics is localized on the symmetry boundary of the (3+1)d slab. We analyze several examples, and present explicit Chern-Simons-Higgs (CSH) field theories realizing the proliferation transitions. We also examine proliferation transitions that implement gauging of non-invertible one-form symmetry in the parent TQFT. This includes a general construction for ${\rm Rep}(G)$ one-form symmetry for a finite group $G$, and a CSH realization of the non-invertible one-form gauging ${\rm SU}(2)_{10}\rightarrow {\rm Spin}(5)_1$. We discuss which anyons proliferate at these transitions.