Symmetry-violating nucleon-nucleon interactions in the large-$N_c$ expansion

Violations of discrete symmetries such as parity (P) and time-reversal invariance (T) in nuclear systems can be used as precision tests of our understanding of the Standard Model as well as in searches for physics beyond the Standard Model. Even if the form of the symmetry-violating quark interactions are known, their manifestations at the nucleon level is complicated by nonperturbative QCD effects. I will describe how the application of the large-$N_c$ expansion to P- and/or T-violating nucleon-nucleon potentials provides theoretical constraints on the size of various symmetry-violating terms. The resulting hierarchy can help delineate which contributions to the potentials should be most important in phenomenological applications.