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A 4d N=1 Cardy Formula

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arxiv 1904.03455 v2 pith:7A4ZGRW3 submitted 2019-04-06 hep-th

Joonho Kim , Seok Kim , Jaewon Song This is my paper · ORCID
classification hep-th
keywords findindexasymptoticcardyentropylimitmathcalaccounts
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abstract

We study the asymptotic behavior of the (modified) superconformal index for 4d $\mathcal{N} = 1$ gauge theory. By considering complexified chemical potential, we find that the `high-temperature limit' of the index can be written in terms of the conformal anomalies $3c-2a$. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound $1/2 < a/c < 3/2$ for the interacting SCFT is satisfied. We study $\mathcal{N} = 1$ theories that are dual to AdS$_5 \times Y^{p, p}$ and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

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Cited by 6 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. Microstates of AdS$_5$ black holes with hypermultiplets

    hep-th 2025-02 conditional novelty 7.0 of 10

    A new family of rotating AdS5 black holes with nonzero hypermultiplet scalars has horizon entropy matching the superconformal index of the dual SCFTs, at first order in a perturbative expansion around z=1.

  3. Gravitational index, black hole saddle degeneracy, and one-form symmetry

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    The |G|-fold degeneracy of supersymmetric AdS5 black hole index saddles is fixed by the flux-quantized BF coupling of the bulk one-form symmetry and persists unmodified in the decompactified black-brane limit.

  4. Supersymmetric zeta functions and determinants

    hep-th 2025-11 conditional novelty 6.0 of 10

    Residues and special values of supersymmetric zeta functions (built from single-particle indices) are conjectured to reproduce anomaly coefficients, Casimir energies, and central charges across 2d/4d/6d.

  5. Quantum vortices, M2-branes and black holes

    hep-th 2019-08 conditional novelty 6.0 of 10

    The Cardy-limit index for M2-brane theories gives a large-N free energy scaling as N^(3/2) that, after a Legendre transform, matches the entropy of BPS black holes in AdS4 x S7.

  6. Black hole entropy function for toric theories via Bethe Ansatz

    hep-th 2019-08 conditional novelty 6.0 of 10

    Using Bethe Ansatz equations, the authors show that a simple class of solutions reproduces the conjectured entropy function of rotating AdS5 black holes for all toric quiver gauge theories.

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