Nonabelian Twists of the $D_4$ Theory

TL;DR

This paper explores nonabelian automorphism twists in $D_4$ class-S theories, extending superconformal index formulas, classifying SCFTs, and revealing new behaviors such as multiple weakly-coupled descriptions for certain punctured spheres.

Contribution

It extends superconformal index formulas to nonabelian twists, classifies new SCFTs, and uncovers novel phenomena like multiple dual descriptions in twisted sectors.

Findings

Extended superconformal index formulas for nonabelian twists.

Classification of SCFTs from fixtures with nonabelian twists.

Discovery of six distinct weakly-coupled descriptions for certain 4-punctured spheres.

Abstract

We study theories of type $D_4$ in class-S, with nonabelian outer-automorphism twists around various cycles of the punctured Riemann surface $C$. We propose an extension of previous formul\ae\ for the superconformal index to cover this case and classify the SCFTs corresponding to fixtures (3-punctured spheres). We then go on to study families of SCFTs corresponding to once-punctured tori and 4-punctured spheres. These exhibit new behaviours, not seen in previous investigations. In particular, the generic theory with 4 punctures on the sphere from non-commuting $\mathbb{Z}_2$ twisted sectors has six distinct weakly-coupled descriptions.