Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups

Dorigoni, Daniele; Green, Michael; Wen, Congkao

doi:10.21468/SciPostPhys.13.4.092

SciPost Physics

Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups

Daniele Dorigoni, Michael B. Green, Congkao Wen

SciPost Phys. 13, 092 (2022) · published 11 October 2022

doi: 10.21468/SciPostPhys.13.4.092
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Abstract

We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\cN=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$, $SO(2N+1)$, $USp(2N)$. These integrated correlators are expressed as two-dimensional lattice sums by considering derivatives of the localised partition functions, generalising the expression obtained for $SU(N)$ \mbg{gauge group} in our previous works. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality. The integrated correlators can also be formally written as infinite sums of non-holomorphic Eisenstein series with integer indices and rational coefficients. Furthermore, the action of the hyperbolic Laplace operator with respect to the complex coupling $\tau=\theta/(2\pi) + 4\pi i /g^2_{_{YM}}$ on any integrated correlator for gauge group $G_N$ relates it to a linear combination of correlators with gauge groups $G_{N+1}$, $G_N$ and $G_{N-1}$. These ``Laplace-difference equations'' determine the expressions of integrated correlators for all classical gauge groups for any value of $N$ in terms of the correlator for the gauge group $SU(2)$. The perturbation expansions of these integrated correlators for any finite value of $N$ agree with properties obtained from perturbative Yang--Mills quantum field theory, together with various multi-instanton calculations which are also shown to agree with those determined by supersymmetric localisation. The coefficients of terms in the large-$N$ expansion are sums of non-holomorphic Eisenstein series with half-integer indices, which extend recent results and make contact with low order terms in the low energy expansion of type IIB superstring theory in an $AdS_5\times S^5/\mathbb{Z}_2$ background.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.4.092
TI  - Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups
PY  - 2022/10/11
UR  - https://scipost.org/SciPostPhys.13.4.092
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 4
SP  - 092
A1  - Dorigoni, Daniele
AU  - Green, Michael
AU  - Wen, Congkao
AB  - We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\cN=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$, $SO(2N+1)$, $USp(2N)$. These integrated correlators are expressed as two-dimensional lattice sums by considering derivatives of the localised partition functions, generalising the expression obtained for $SU(N)$ \mbg{gauge group} in our previous works. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality. The integrated correlators can also be formally written as infinite sums of non-holomorphic Eisenstein series with integer indices and rational coefficients. Furthermore, the action of the hyperbolic Laplace operator with respect to the complex coupling $\tau=\theta/(2\pi) + 4\pi i /g^2_{_{YM}}$ on any integrated correlator for gauge group $G_N$ relates it to a linear combination of correlators with gauge groups $G_{N+1}$, $G_N$ and $G_{N-1}$. These ``Laplace-difference equations'' determine the expressions of integrated correlators for all classical gauge groups for any value of $N$ in terms of the correlator for the gauge group $SU(2)$. The perturbation expansions of these integrated correlators for any finite value of $N$ agree with properties obtained from perturbative Yang--Mills quantum field theory, together with various multi-instanton calculations which are also shown to agree with those determined by supersymmetric localisation. The coefficients of terms in the large-$N$ expansion are sums of non-holomorphic Eisenstein series with half-integer indices, which extend recent results and make contact with low order terms in the low energy expansion of type IIB superstring theory in an $AdS_5\times S^5/\mathbb{Z}_2$ background.
ER  -

@Article{10.21468/SciPostPhys.13.4.092,
	title={{Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups}},
	author={Daniele Dorigoni and Michael B. Green and Congkao Wen},
	journal={SciPost Phys.},
	volume={13},
	pages={092},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.4.092},
	url={https://scipost.org/10.21468/SciPostPhys.13.4.092},
}

Cited by 14

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J. High Energ. Phys. 2023, 203 (2023) [Crossref]
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J. High Energ. Phys. 2022, 48 (2022) [Crossref]
Beccaria et al., Exact strong coupling results in $$ \mathcal{N} $$ = 2 Sp(2N) superconformal gauge theory from localization
J. High Energ. Phys. 2023, 37 (2023) [Crossref]
Hatsuda et al., Large N expansion of an integrated correlator in $$ \mathcal{N} $$ = 4 SYM
J. High Energ. Phys. 2022, 86 (2022) [Crossref]
Brown et al., Laplace-difference equation for integrated correlators of operators with general charges in $$ \mathcal{N} $$ = 4 SYM
J. High Energ. Phys. 2023, 66 (2023) [Crossref]
Brown et al., Integrated Correlators in N=4 Supersymmetric Yang-Mills Theory beyond Localization
Phys. Rev. Lett. 132, 101602 (2024) [Crossref]
Paul et al., Integrated correlators in $$ \mathcal{N} $$ = 4 SYM via SL(2, ℤ) spectral theory
J. High Energ. Phys. 2023, 149 (2023) [Crossref]
Dorigoni et al., Modular-invariant large-N completion of an integrated correlator in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory
J. High Energ. Phys. 2023, 114 (2023) [Crossref]
Behan et al., Gluon scattering in AdS at finite string coupling from localization
J. High Energ. Phys. 2024, 42 (2024) [Crossref]
Brown et al., Generating functions and large-charge expansion of integrated correlators in 𝒩 = 4 supersymmetric Yang-Mills theory
J. High Energ. Phys. 2023, 129 (2023) [Crossref]
Dorigoni et al., Two string theory flavours of generalised Eisenstein series
J. High Energ. Phys. 2023, 102 (2023) [Crossref]
Cavaglià et al., Integrated correlators from integrability: Maldacena-Wilson line in $$ \mathcal{N} $$ = 4 SYM
J. High Energ. Phys. 2023, 26 (2023) [Crossref]
Billò et al., Integrated correlators with a Wilson line in $$ \mathcal{N} $$ = 4 SYM
J. High Energ. Phys. 2023, 47 (2023) [Crossref]
Billò et al., A matrix-model approach to integrated correlators in a $$ \mathcal{N} $$ = 2 SYM theory
J. High Energ. Phys. 2024, 154 (2024) [Crossref]

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Daniele Dorigoni,
² ³ Michael Green,
² Congkao Wen

Funder for the research work leading to this publication

Royal Society