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PreprintCC BY 4.0arXiv

Giant Graviton Expansions from Symmetric Functions and Free Fermions

  • Min-xin Huang
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Abstract

Giant graviton expansions express finite-rank corrections to supersymmetric indices in terms of indices for wrapped D3-branes. We give detailed algebraic proofs of two previously proposed relations for four-dimensional 𝒩=4 U(N) super-Yang--Mills theory. The first is the Gaiotto--Lee single-sum expansion of the full superconformal index, proved by Hall--Littlewood orthogonality and an elementary calculation of operator traces. The second is the symmetric double-sum expansion of the flavored Schur index, proved by factorizing its exact free-fermion mode product. We specify the analytic continuation of the brane indices and justify the sums coefficient by coefficient. The two proofs apply to different expansion prescriptions and do not establish the full three-species expansion of Imamura. We discuss the additional physical and mathematical questions raised by that expansion and by the modular properties of the Schur index.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026giant,
  title = {{Giant Graviton Expansions from Symmetric Functions and Free Fermions}},
  author = {Min-xin Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18452},
  eprint = {2610.18452},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18452},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Giant Graviton Expansions from Symmetric Functions and Free Fermions
AU  - Min-xin Huang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18452
UR  - https://arxiv.org/abs/2610.18452
AB  - Giant graviton expansions express finite-rank corrections to supersymmetric indices in terms of indices for wrapped D3-branes. We give detailed algebraic proofs of two previously proposed relations for four-dimensional 𝒩=4 U(N) super-Yang--Mills theory. The first is the Gaiotto--Lee single-sum expansion of the full superconformal index, proved by Hall--Littlewood orthogonality and an elementary calculation of operator traces. The second is the symmetric double-sum expansion of the flavored Schur index, proved by factorizing its exact free-fermion mode product. We specify the analytic continuation of the brane indices and justify the sums coefficient by coefficient. The two proofs apply to different expansion prescriptions and do not establish the full three-species expansion of Imamura. We discuss the additional physical and mathematical questions raised by that expansion and by the modular properties of the Schur index.
ER  -