Exact results for giant graviton four-point correlators

Abstract We study the four-point correlator O 2 O 2 DD $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle $$ in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where O 2 $$ {\mathcal{O}}_2 $$ represents the superconformal primary operator with dimen...

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Main Authors: Augustus Brown, Francesco Galvagno, Congkao Wen
Format: Article
Language:English
Published: SpringerOpen 2024-07-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP07(2024)049
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author Augustus Brown
Francesco Galvagno
Congkao Wen
author_facet Augustus Brown
Francesco Galvagno
Congkao Wen
author_sort Augustus Brown
collection DOAJ
description Abstract We study the four-point correlator O 2 O 2 DD $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle $$ in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where O 2 $$ {\mathcal{O}}_2 $$ represents the superconformal primary operator with dimension two, while D $$ \mathcal{D} $$ denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S 5. 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 N $$ \mathcal{N} $$ = 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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spelling doaj-art-090e4adb156248ffa6c0ab6d78ebcdbc2025-08-20T02:11:22ZengSpringerOpenJournal of High Energy Physics1029-84792024-07-012024714810.1007/JHEP07(2024)049Exact results for giant graviton four-point correlatorsAugustus Brown0Francesco Galvagno1Congkao Wen2Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonCentre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonCentre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonAbstract We study the four-point correlator O 2 O 2 DD $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle $$ in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where O 2 $$ {\mathcal{O}}_2 $$ represents the superconformal primary operator with dimension two, while D $$ \mathcal{D} $$ denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S 5. 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 N $$ \mathcal{N} $$ = 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.https://doi.org/10.1007/JHEP07(2024)0491/N ExpansionExtended SupersymmetryMatrix Models
spellingShingle Augustus Brown
Francesco Galvagno
Congkao Wen
Exact results for giant graviton four-point correlators
Journal of High Energy Physics
1/N Expansion
Extended Supersymmetry
Matrix Models
title Exact results for giant graviton four-point correlators
title_full Exact results for giant graviton four-point correlators
title_fullStr Exact results for giant graviton four-point correlators
title_full_unstemmed Exact results for giant graviton four-point correlators
title_short Exact results for giant graviton four-point correlators
title_sort exact results for giant graviton four point correlators
topic 1/N Expansion
Extended Supersymmetry
Matrix Models
url https://doi.org/10.1007/JHEP07(2024)049
work_keys_str_mv AT augustusbrown exactresultsforgiantgravitonfourpointcorrelators
AT francescogalvagno exactresultsforgiantgravitonfourpointcorrelators
AT congkaowen exactresultsforgiantgravitonfourpointcorrelators