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The giant graviton expansion in $AdS_5 \times S^5$

by Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló

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Submission summary

Authors (as registered SciPost users): Sameer Murthy
Submission information
Preprint Link: https://arxiv.org/abs/2312.14921v4  (pdf)
Date accepted: 2024-09-13
Date submitted: 2024-08-17 19:44
Submitted by: Murthy, Sameer
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory

Abstract

The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual $AdS_5 \times S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.

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  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission

Changes made as requested.

List of changes

Added comment on the M2 and M5-brane theories at the end of the paper. Typos corrected as listed on the SciPost page.

Published as SciPost Phys. 17, 098 (2024)


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Anonymous Report 1 on 2024-8-31 (Invited Report)

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