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The superconformal index of $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM as a matrix integral

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arxiv 2012.15208 v3 pith:CHZFXADG submitted 2020-12-30 hep-th

Antonio Amariti , Marco Fazzi , Alessia Segati This is my paper · ORCID
classification hep-th
keywords indexmatrixcaseintegralcomputeentropygaugegroup
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the superconformal index of 4d $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point solution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the $USp(2N_c)$ case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with $SU(N_c)$ gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.

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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. Probing Non-Graviton Spectra in $\mathcal{N}=4$ SYM via BMN truncation and S-Duality

    hep-th 2025-06 conditional novelty 7.0 of 10

    The BMN index of N=4 SYM contains universal non-graviton bosonic towers, and the S-duality mismatch between SO(7) and Sp(3) pinpoints a non-graviton cohomology.

  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.

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