Breaking discrete symmetries in broken gauge theories

We study the spontaneous breaking of discrete symmetries in theories with broken gauge symmetry. The intended application is to CP breaking in theories with gauged flavor symmetries, but the analysis described here is preliminary. We dispense with matter fields and take the gauge theory to be weakly coupled and broken spontaneously by unspecified, short-distance forces. We develop an effective-field-theory description of the resultant low-energy theory, and ask whether this theory by itself can describe the subsequent breaking of discrete symmetries. We conclude that this can happen depending on the parameters of the effective theory, and that the intrinsic violation is naturally of order unity.