A Bulk-Boundary Correspondence for 2D Fermionic 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 general method for solving this problem in the case of (2+1)D interacting Fermionic systems with internal (non-spatial) symmetries.