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.