New Dualities and Misleading Anomaly Matchings from Outer-automorphism Twists

TL;DR

This paper explores how outer-automorphism twists in 4d N=1 superconformal theories derived from 6d theories lead to multiple dual descriptions, revealing cases where anomaly matching alone cannot confirm dualities.

Contribution

It introduces new dualities arising from twist line configurations in class S theories and demonstrates that anomalies may not distinguish all dual pairs.

Findings

Different twist line configurations produce dual theories with identical anomalies.

Superconformal indices can differ even when anomalies match.

Outer-automorphism twists lead to misleading anomaly matchings.

Abstract

We study four-dimensional N=1, 2 superconformal theory in class S obtained by compactifying the 6d N=(2, 0) theory on a Riemann surface C with outer-automorphism twist lines. From the pair-of-pants decompositions 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 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 set of examples where the anomaly matching is insufficient to test dualities.