Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs

TL;DR

This paper derives a universal formula for the Cardy-like limit of the superconformal index in 4d $ abla=1$ SCFTs with ABCD gauge groups, extending previous results and validating it through multiple examples.

Contribution

It introduces a universal formula for the superconformal index's behavior in the Cardy-like limit for a broad class of $ abla=1$ SCFTs, generalizing prior specific cases.

Findings

The formula captures the index behavior at finite rank and fugacities.

Validation through examples beyond toric classes.

Applicability to models without weakly-coupled gravity duals.

Abstract

We study the Cardy-like limit of the superconformal index of generic $\mathcal{N}=1$ SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.