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<p>We consider giant gravitons in the probe approximation when they are described by classical brane configurations in AdS<sub><i>p</i>+2</sub> × <i>S</i><sup><i>q</i>+2</sup> wrapping a particular <i>q</i>-cycle and spinning in <i>S</i><sup><i>q</i>+2</sup>. We quantize the full set of fluctuations of these configurations and show that they are sufficient to capture all the supersymmetric single-letter indices of the corresponding dual field theories. We explicitly discuss the cases of D3, M2 and M5 branes and reproduce the single-letter indices for all fractions of supersymmetry. We also provide a new derivation of the full finite-<i>N</i> half-BPS index by promoting certain fluctuations to matrix-valued fields. We elaborate on the obstructions for the general finite-<i>N</i> computations. Given that the single-letter partition functions are the building blocks of all supersymmetric enumerations, including for the black hole entropy, our work provides a direct gravitational counting of those degrees of freedom modulo finite-<i>N</i> obstacles due to non-Abelian effects.</p>

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Quantized giant gravitons as the periodic table of supersymmetric states: D3, M2 and M5

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月7日

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  • Evan Deddo,
  • Sabarenath Jayaprakash,
  • James T. Liu,
  • Leopoldo A. Pando Zayas

摘要

We consider giant gravitons in the probe approximation when they are described by classical brane configurations in AdSp+2 × Sq+2 wrapping a particular q-cycle and spinning in Sq+2. We quantize the full set of fluctuations of these configurations and show that they are sufficient to capture all the supersymmetric single-letter indices of the corresponding dual field theories. We explicitly discuss the cases of D3, M2 and M5 branes and reproduce the single-letter indices for all fractions of supersymmetry. We also provide a new derivation of the full finite-N half-BPS index by promoting certain fluctuations to matrix-valued fields. We elaborate on the obstructions for the general finite-N computations. Given that the single-letter partition functions are the building blocks of all supersymmetric enumerations, including for the black hole entropy, our work provides a direct gravitational counting of those degrees of freedom modulo finite-N obstacles due to non-Abelian effects.