New dualities and misleading anomaly matchings from outer-automorphism twists

Abstract

We study four-dimensional N - 1, 2 superconformal theories in class S ob-tained by compactifying the 6d N = ( 2, 0) theory on a Riemann surface C with outer-automorphism twist lines. From the pair-of-pants decompositions of C, we find various dual descriptions for the same theory having distinct gauge groups. We show that the various configurations of the twist line give rise to dual descriptions for the identical the-ory. We compute the ' t Hooft anomaly coefficients and the superconformal indices to test dualities. Surprisingly, we find that the class S theories with twist lines wrapping 1-cycles of C have the identical ' t Hooft anomalies as the ones without the twist line, whereas the superconformal indices differ. This provides a large set of examples where the anomaly matching is insufficient to test dualities.