Geometric Categories for Continuous Gauging

Abstract: We present a unified categorical framework which encodes gauging of continuous and finite symmetries in arbitrary spacetime dimension. We show that electric symmetry breaking, resulting from the addition of charged matter, is implemented by this gauging procedure, and identify electric and magnetic symmetries expected in $G$-gauge theory. We work with geometric categories, i.e. categories internal to stacks. This allows us to extend (de)equivariantization of fusion categories to continuous groups, construct a functorial SymTFT and boundaries for this theory, and compute the relevant categories of endomorphisms and Drinfeld centers.