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The large $N$ limit of topologically twisted indices: a direct approach

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arxiv 2209.09274 v1 pith:6AWXPKHF submitted 2022-09-19 hep-th

Seyed Morteza Hosseini , Alberto Zaffaroni This is my paper · ORCID
classification hep-th
keywords largetwistedblackchargeddirectgaugeholesindex
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We study the large $N$ limit of the refined topologically twisted index of three-dimensional $\mathcal{N} = 2$ gauge theories with a holographic dual, which is relevant for counting the number of microstates of rotating, magnetically charged and twisted AdS$_4$ black holes. As a difference with previous computations, we perform a direct saddle point analysis of the relevant matrix model. Among other things we explicitly identify the distribution of gauge magnetic fluxes that contributes at large $N$. The index exhibits a large $N$ factorized form in agreement with the supergravity expectations based on gravitational blocks and correctly reproduces the entropy of magnetically charged rotating AdS$_4 \times S^7$ black holes.

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Cited by 3 Pith papers

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  1. Equivariant localization for $D=4$ gauged supergravity

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    Supersymmetric Euclidean D=4 N=2 gauged supergravity actions and fluxes localize onto R-symmetry fixed points, proving large-N SCFT free-energy formulas and UV-IR relations.

  2. Exact Modular Completion of the ABJM Effective Twisted Superpotential

    hep-th 2026-08 conditional novelty 7.0 of 10

    The paper reports closed-form and apparently exact formulas, involving Eisenstein series and Eichler integrals, for the nonperturbative completion of the ABJM twisted superpotential at levels 1, 2, and 4.

  3. $\mathcal{I}$-Extremization for AdS$_4$ Black Holes: Master Volume, Free Energy, and Baryonic Charges

    hep-th 2025-05 conditional novelty 6.0 of 10

    For toric AdS4 black holes, the geometric entropy extremization of Gauntlett, Martelli and Sparks is shown to be equivalent to I-extremization with a generalized free energy built from the master volume, including bar...

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