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Giant Graviton Integrated Correlators at Finite Coupling and All Orders in 1/N

Augustus Brown1, Daniele Dorigoni2,*, and Congkao Wen1

  • 1Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, United Kingdom
  • 2Centre for Particle Theory and Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom

  • *Contact author: daniele.dorigoni@durham.ac.uk
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Phys. Rev. Lett. 137, 101601 – Published 3 September, 2026

DOI: https://doi.org/10.1103/15r8-grqb

Abstract

We study the giant graviton integrated correlator in SU(N) N=4 super-Yang-Mills at finite complexified coupling τ. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-N expansion simplifies dramatically and exhibits manifest modular invariance. At each order in 1/N, the expansion coefficients are linear combinations of nonholomorphic Eisenstein series, thus capturing the full spectrum of perturbative and nonperturbative effects in the Yang-Mills coupling. Furthermore, we find additional contributions, which are modular functions exponentially suppressed in N. In the ’t Hooft limit, this yields an all-orders result in the 1/N expansion at arbitrary coupling λ, extending beyond prior results of leading orders. For the U(N) theory, we obtain a closed-form expression valid for all N and τ and show that the coupling-dependent sector of the large-N expansion is universal between SU(N) and U(N) to all orders. Crucially, we exploit the integrated correlator constraints and determine the giant graviton correlator itself to two-loop order at finite N, previously only accessible in the planar limit.

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Outline

Information

Phys. Rev. Lett. 137, 101601– Published 3 September, 2026
  • Received 15 April 2026
  • Accepted 10 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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