Abstract
We evaluate the topologically twisted index of a general four-dimensional \( \mathcal{N}=1 \) gauge theory in the “high-temperature” limit. The index is the partition function for \( \mathcal{N}=1 \) 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 \( \mathcal{N}=\left(0,2\right) \) 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.
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Hosseini, S.M., Nedelin, A. & Zaffaroni, A. The Cardy limit of the topologically twisted index and black strings in AdS5 . J. High Energ. Phys. 2017, 14 (2017). https://doi.org/10.1007/JHEP04(2017)014
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DOI: https://doi.org/10.1007/JHEP04(2017)014