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6d superconformal Cardy formulas

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 $AdS_7$.