6d superconformal Cardy formulas

TL;DR

The paper develops a unified, anomaly-based framework to obtain Cardy-limit formulas for the 6d superconformal index. By linking the index to the 6d anomaly polynomial via a thermal CS action and the thermal anomaly polynomial P_8^T (or equivalently its equivariant integral), it derives explicit Cardy formulas for general 6d theories and concrete families (1,0, ADE (2,0), E-string, M5 on ALE). The results reproduce known indices where available, uncover N^3 growth in large-N cases, and match the entropy of supersymmetric AdS_7 black holes, while revealing a universal bound a−4 b+16 c≥0 on anomaly coefficients. The work thus unifies index computations, anomaly data, and holographic entropy in six dimensions, providing a practical toolkit for analyzing broad classes of 6d SCFTs.

Abstract

We study the superconformal index of 6d SCFTs from their 't Hooft anomalies. In the Cardy limit where the angular momenta on $S^5$ are large, we show that the leading free energy, as well as a few subleading corrections, can be computed from the 6d anomaly polynomials. Our large $N$ free energy accounts for the entropy of supersymmetric black holes in dual $AdS_7$.