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 × 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 IIB backgrounds AdS5 × SE5, where SE5 are five-dimensional Sasaki-Einstein spaces.