Abstract
We study four-dimensional mathcal{N}=1, 2 superconformal theories in class mathcal{S} obtained by compactifying the 6d mathcal{N}=left(2, 0right) theory on a Riemann surface mathcal{C} with outer-automorphism twist lines. From the pair-of-pants decompositions of mathcal{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 theory. We compute the ’t Hooft anomaly coefficients and the superconformal indices to test dualities. Surprisingly, we find that the class mathcal{S} theories with twist lines wrapping 1-cycles of mathcal{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.
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