Gauging (3+1)-dimensional topological phases: an approach from surface theories
Abstract
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)d 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 point-like and loop-like 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.