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We explore the supersymmetric partition functions of 6d SCFTs on$\mathbb{R}^4\times T^2$ with non-vanishing charges for compatible globalsymmetries. We utilize the elliptic genera for self-dual strings and computethe 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 theorigin of $N^3$ comes from the condensation of the self-dual strings, whosetotal number is proportional to ${N^3-N\over 6}$. We further extend ouranalysis to the general E-string theory and obtain its Cardy free energy.

Cardy Limits of 6d Superconformal Theories