We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Exact results for duality-covariant integrated correlators in N=4 SYM with general classical gauge groups

Dorigoni, Daniele and Green, Michael B. and Wen, Congkao (2022) 'Exact results for duality-covariant integrated correlators in N=4 SYM with general classical gauge groups.', SciPost Physics .


We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of N = 4 supersymmetric Yang–Mills (SYM) theory with classical gauge group, GN = 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) 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 τ = θ/(2π)+ 4πi/g2 Y M on any integrated correlator for gauge group GN relates it to a linear combination of correlators with gauge groups GN+1, GN and GN−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 nonholomorphic 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 AdS5 × S5/Z2 background.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution 4.0.
Download PDF
Publisher Web site:
Publisher statement:The article is distributed under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Unless otherwise stated, any associated published material is distributed under the same license. If one or more authors are US government employees, the paper can be published under the terms of the Creative Commons CC0 public domain dedication.
Date accepted:30 August 2022
Date deposited:07 October 2022
Date of first online publication:2022
Date first made open access:07 October 2022

Save or Share this output

Look up in GoogleScholar