Three ways to gauge symmetry in 3D quantum field theory, compared

Gauging a symmetry — promoting it from a global to a local structure — is a central tool in quantum field theory, but different algebraic frameworks for doing it can look unrecognizable from one another. Working through explicit models including Dijkgraaf–Witten theory, Tambara–Yamagami categories, and Chern–Simons SU(2)_k theory, this paper maps the relationships among equivariantisation, G-crossed braided zesting, and the generalised orbifold construction. A key result is that zested orbifold data, while superficially distinct, are Morita-equivalent — they define the same surface defect. This unification clarifies when symmetry gauging is obstructed and provides a practical toolkit for comparing results across formalisms.