Operator spectroscopy for 4d SCFTs with a=c

TL;DR

This paper investigates 4d superconformal field theories with equal central charges, constructed via gauging flavor symmetries of Argyres-Douglas theories, and analyzes their operator content and IR behavior.

Contribution

It introduces a class of 4d SCFTs with a=c constructed through gauging Argyres-Douglas theories and provides detailed index computations and operator analysis.

Findings

Most theories flow to interacting SCFTs with a=c in the IR.

Superconformal indices computed for low-rank cases support unitarity.

Detailed operator content and marginal operators identified.

Abstract

We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting SCFTs with $a=c$ in the infrared.