Central charges from the $\mathcal{N} = 1$ superconformal index

TL;DR

This paper introduces methods to derive the central charges of 4D superconformal theories from the superconformal index, enabling precise AdS/CFT matching and extending applicability beyond holographic and large-N regimes.

Contribution

It provides novel prescriptions to extract the central charges from the superconformal index, including exact AdS/CFT matching for toric quiver CFTs without adjoint matter.

Findings

Exact AdS/CFT matching of central charges for certain theories.

Prescriptions applicable to non-holographic and finite-N theories.

Evidence supporting broader applicability of the methods.

Abstract

We present prescriptions for obtaining the central charges, $a$ and $c$, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite $N$, for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the $\mathcal{O}(1)$ parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of $a$ and $c$ for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of these results outside of a holographic setting and away from the large-$N$ limit.