Gauging (3+1)-dimensional topological phases: An approach from surface theories

We discuss several bosonic topological phases in (3+1) dimensions enriched by a global Z₂ symmetry, and gauging the Z₂ symmetry. More specifically, following the spirit of the bulk-boundary correspondence, expected to hold in topological phases of matter in general, we consider boundary (surface) field theories and their orbifold. From the surface partition functions, we extract the modular S and T matrices and compare them with $(2+1)$-dimensional toplogical phase after dimensional reduction. As a specific example, we discuss topologically ordered phases in $(3+1)$ dimensions described by the BF topological quantum field theories, with abelian exchange statistics between pointlike and looplike quasiparticles. Once the Z₂ charge conjugation symmetry is gauged, the Z₂ flux becomes non-Abelian excitation. The gauged topological phases we are considering here belong to the quantum double model with non-Abelian group in $(3+1)$ dimensions.