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Universal 3d Cardy Block and Black Hole Entropy

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arxiv 1911.01448 v3 pith:DBHWDAZ7 submitted 2019-11-04 hep-th

Sunjin Choi , Chiung Hwang This is my paper · ORCID
classification hep-th
keywords cardyblockindexpartitionfunctionslimituniversaldiscuss
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abstract

We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition function. In the Cardy limit, the hemisphere index can be evaluated by the saddle point approximation where there exists a dominant saddle point contribution, which we call the Cardy block. The Cardy block turns out to be a simple but powerful object as it is a building block of other partition functions in the Cardy limit. The factorization to the Cardy block allows us to find universal relations among the partition functions, which we formulate as index theorems. Furthermore, if we consider a holographic 3d SCFT and its large $N$ limit, those partition functions relate to various entropic quantities of the dual gravity theory in AdS$_4$. As a result, our result provides the microscopic derivation of the universal relations among those entropic quantities of the gravity theory. We also discuss explicit examples, which confirm our general index theorems.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cardy limit of the 3d superconformal index

    hep-th 2025-09 conditional novelty 8.0 of 10

    In the Cardy limit the 3d superconformal index obeys Z ~ beta^{-#} on the first sheet and Z ~ e^{#/beta} on the second, with gauge-enhancing saddles screened for non-chiral theories.

  2. Ten-dimensional localization

    hep-th 2026-07 conditional novelty 7.0 of 10

    Equivariantly closed polyforms for type II Page fluxes and actions enable direct 10D localization of on-shell actions and flux quantization for minimally supersymmetric backgrounds.

  3. Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes

    hep-th 2024-12 conditional novelty 7.0 of 10

    Near-BPS dyonic AdS4 black holes with a theta angle show a Witten-effect charge shift that reduces the mass gap and the index, and at the special angle both the Bekenstein-Hawking entropy and the supersymmetric index ...

  4. An Airy Tale at Large $N$

    hep-th 2025-02 conditional novelty 6.0 of 10

    The paper presents numerical and analytic evidence that the large-N sphere partition function of five classes of M2-brane SCFTs, with squashing and real masses, takes the form of an Airy function to all orders in 1/N.

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