Charting Class ${\cal S}_k$ Territory

TL;DR

This paper explores a large family of 4d $ ext{SCFT}$s within class ${ m S}_k$, revealing new features like non-trivial anomalous dimensions, novel gluing methods, and duality structures related to 6d theories and superconformal indices.

Contribution

It systematically studies the ${ m S}_k^1$ class of theories, uncovering their dualities, anomalous dimensions, and connections to 6d ${ m T}_N^k$ theories via orbifold constructions and puncture manipulations.

Findings

Identification of non-trivial anomalous dimensions.

Description of dualities via puncture exchange and Seiberg duality.

Verification of dualities through superconformal index computations.

Abstract

We extend the investigation of the recently introduced class ${\cal S}_k$ of 4d $\mathcal{N}=1$ SCFTs, by considering a large family of quiver gauge theories within it, which we denote $\mathcal{S}^1_k$. These theories admit a realization in terms of $\mathbb{Z}_k$ orbifolds of Type IIA configurations of D4-branes stretched among relatively rotated sets of NS-branes. This fact permits a systematic investigation of the full family, which exhibits new features such as non-trivial anomalous dimensions differing from free field values and novel ways of gluing theories. We relate these ingredients to properties of compactification of the 6d (1,0) superconformal ${\cal T}_N^k$ theories on spheres with different kinds of punctures. We describe the structure of dualities in this class of theories upon exchange of punctures, including transformations that correspond to Seiberg dualities, and exploit the computation of the superconformal index to check the invariance of the theories under them.