Abstract
We study the four-point correlator \( \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle \) in \( \mathcal{N} \) = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where \( {\mathcal{O}}_2 \) represents the superconformal primary operator with dimension two, while \( \mathcal{D} \) denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S5. We analyse the integrated correlator associated with this observable, obtained after integrating out the spacetime dependence over a supersymmetric invariant measure. Similarly to other classes of integrated correlators in \( \mathcal{N} \) = 4 SYM, this integrated correlator can be computed through supersymmetric localisation on the four-sphere. Employing matrix-model recursive techniques, we demonstrate that the integrated correlator can be reformulated as an infinite sum of protected three-point functions with known coefficients. This insight allows us to circumvent the complexity associated with the dimension-N determinant operator, significantly streamlining the large-N expansion of the integrated correlator. In the planar limit and beyond, we derive exact results for the integrated correlator valid for all values of the ’t Hooft coupling, and investigate the resurgent properties of their strong coupling expansion. Additionally, in the large-N expansion with fixed (complexified) Yang-Mills coupling, we deduce the SL(2, ℤ) completion of these results in terms of the non-holomorphic Eisenstein series. The proposed modular functions are confirmed by explicit instanton calculations from the matrix model, and agree with expectations from the holographic dual picture of known results in type IIB string theory.
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Acknowledgments
We would like to thank Marco Billó, Frank Coronado, Robert de Mello Koch, Daniele Dorigoni, Zhihao Duan, Marialuisa Frau, Alessandro Georgoudis, Michael Green, Paul Heslop, Yunfeng Jiang, Shota Komatsu, Alberto Lerda, Sanjaye Ramgoolam, Rodolfo Russo, Oliver Schlotterer, Yu Wu, and Yang Zhang for many useful discussions and comments on the draft.
A.B. is supported by a Royal Society funding RF\ERE\210067. C.W. is supported by a Royal Society University Research Fellowship, URF\R\221015. F.G. and C.W. are supported by a STFC Consolidated Grant, ST\T000686\1 “Amplitudes, strings & duality”.
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Brown, A., Galvagno, F. & Wen, C. Exact results for giant graviton four-point correlators. J. High Energ. Phys. 2024, 49 (2024). https://doi.org/10.1007/JHEP07(2024)049
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DOI: https://doi.org/10.1007/JHEP07(2024)049