Cardy limits of 6d superconformal theories

We explore the supersymmetric partition functions of 6d SCFTs on R-4 x 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 N3-N/6. We further extend our analysis to the general E-string theory and obtain its Cardy free energy.