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Proving the 6d Cardy formula and matching global gravitational anomalies

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Summary: This study examines the asymptotic behavior of the (modified) superconformal index for 4d N = 1 gauge theory, finding that the 'high-temperature limit' of the index can be expressed in terms of conformal anomalies. Moreover, the macroscopic entropy of the interacting SCFT system is derived from the asymptotic free energy when certain bounds are satisfied. Additionally, the Carby limit of the index for N = 1 theories dual to AdS(5) x Y-p,Y-p is found to explain the Bekenstein-Hawking entropy of large black holes.

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