We initiate the study of the effects of strong 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 show how the S-duality of N=2 supersymmetric SU(2) gauge theory with Nf=4 flavors can be used to show the
mod 16 behavior of topological superconductors.