't Hooft Anomaly Matching for Discrete Symmetries

We show how to extend the 't Hooft anomaly matching conditions to discrete symmetries. We check these discrete anomaly matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N=1 supersymmetric Yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N=1 supersymmetric theories based on exceptional groups.