Cardy Limits of 6d Superconformal Theories

TL;DR

This paper investigates the behavior of 6d superconformal field theories' partition functions in the Cardy limit, revealing an N^3 scaling linked to self-dual string condensation, with extensions to E-string theories.

Contribution

It provides a novel computation of the Cardy limit free energy for 6d SCFTs, elucidating the origin of N^3 scaling from self-dual string dynamics and extending results to E-string theories.

Findings

Free energy scales as N^3 for 6d (2,0) theories.

Self-dual string condensation accounts for N^3 behavior.

Results extend to E-string theories in the Cardy limit.

Abstract

We explore the supersymmetric partition functions of 6d SCFTs on $\mathbb{R}^4\times T^2$ with non-vanishing charges for compatible global symmetries. We utilize the elliptic genera for self-dual strings and compute the free energy of 6d SCFTs in the Cardy limit. For a 6d (2,0) theory on $N$ M5-brane, we obtain the free energy proportional to $N^3$. We find that the origin of $N^3$ comes from the condensation of the self-dual strings, whose total number is proportional to ${N^3-N\over 6}$. We further extend our analysis to the general E-string theory and obtain its Cardy free energy.