A bulk-boundary correspondence for 3D bosonic symmetry protected topological phases

A universal property of symmetry protected topological (SPT) phases is that they have low energy boundary modes that are protected under the symmetry. This fact inspires an important problem in the theory of SPT phases: How does one identify a bulk SPT phase given a low energy theory of its boundary? This question is particularly challenging in the case of interacting SPT phases where band theory approaches are inapplicable. In this talk, we present a method for solving this problem in the case of gapless boundaries of (3+1)D interacting bosonic systems. This solution centers around the calculation of generalized F-symbols for string like domain wall excitations in the boundary theory which are then identified with an important bulk topological invariant.