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Bootstrapping giant graviton correlators

Song He (何颂)1,2,*, Canxin Shi (施灿欣)1,†, Yichao Tang (唐一朝)1,3,‡, and Congkao Wen (温从烤)4,§

  • *Contact author: songhe@itp.ac.cn
  • †Contact author: shicanxin@itp.ac.cn
  • ‡Contact author: tangyichao@itp.ac.cn
  • §Contact author: c.wen@qmul.ac.uk
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Phys. Rev. D 114, 046029 – Published 26 August, 2026

DOI: https://doi.org/10.1103/9nr9-5y4f

Abstract

We develop bootstrap methods for mixed heavy-light four-point correlators ⟨GGOO⟩ in N=4 super-Yang-Mills theory at large N, where O≡O2 is the chiral primary operator in the stress-tensor multiplet and G are (dual) giant graviton operators with dimension of order N, including the maximal determinant case. The loop integrand is expanded in a basis of labeled f-graphs—necessarily including nonplanar topologies due to the dimension-N nature of the giant gravitons—and the coefficients are fixed by various bootstrap conditions, including double-triangle and triangle rules in the cusp and operator product expansion limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries Ok. Together, these inputs uniquely determine the correlator through three loops, passing further nontrivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.

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References (45)

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  39. Since the OO-channel OPE only involves the anomalous dimension of the Konishi operator, which does not receive 1/N corrections up to three loops [26], this analysis also applies at finite N, provided one uses the corresponding finite-N integrated correlators, as in [10].

  40. The result is in agreement with an independent computation of [38]. As commented earlier, this confirms the ten-dimensional hidden symmetry for generic giant gravitons at two loops.

  41. While this manuscript was under revision, Ref. [42] appeared, presenting a computation of the large-spin OPE coefficients for the maximal giant graviton (α=1) with some assumptions of integrability. Their result coincides with the α=1, c=0 specialization of (22). The hidden-symmetry input imposed here instead selects c=−α, and hence c=−1 for the maximal giant graviton.

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  43. This large-spin behavior is consistent with an independent light cone bootstrap analysis. We thank Frank Coronado for private communication on this point.

  44. Many of these f-graph periods at four loops, including nonplanar ones, have been obtained in [45] and were used to verify the localization computation for ⟨O2O2O2O2⟩ beyond the planar limit.

  45. Shun-Qing Zhang, Nonplanar integrated correlator in N=4 SYM, Phys. Rev. D 110, 025003 (2024).

Outline

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Phys. Rev. D 114, 046029– Published 26 August, 2026
  • Received 4 June 2026
  • Accepted 3 August 2026
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