Axion field theory and $Z_{16}$ classification of time reversal invariant topological superconductors

Time-reversal invariant topological superconductors (TRI TSC) are gapped superconductors with topologically robust gapless modes on the boundary. In the work by X. L. Qi et al, [PRB, 87, 134519(2013)], a topological field theory description was proposed for 3+1-dimensional TRI TSC, which contains an axionic coupling between superconducting phase and electromagnetic field. In my talk, I will describe a generalization of this theory to include interaction effects which provides a physical explanation why the integer classification is reduced to $Z_{16}$. I will also attempt to generalize our results to higher dimensions and give constraints on the possible collapsing of topological classification induced by interaction effects.