The Cardy limit of the topologically twisted index and black strings in AdS5

We evaluate the topologically twisted index of a general four-dimensional N = 1 gauge theory in the high-temperature limit. The index is the partition function for N = 1 theories on S-2 x T-2, with a partial topological twist along S-2, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional N = (0, 2) SCFTs obtained from the compactification on S-2. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type JIB backgrounds AdS(5) x SE5, where SE5 are five-dimensional Sasaki-Einstein spaces.