Gauge interactions and topological phases of matter

We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang-Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory with $N_f=4$ flavors to show that the $\nu =16$ phase of Majorana fermions can be continuously connected to the trivial $\nu =0$ phase.