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

Dorigoni, Daniele; Green, Michael B.; Wen, Congkao

Abstract

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.

Citation

Dorigoni, D., Green, M. B., & Wen, C. (2022). Exact results for duality-covariant integrated correlators in N=4 SYM with general classical gauge groups. SciPost Physics, 13, Article 092(2022). https://doi.org/10.21468/scipostphys.13.4.092

• Journal Article Type: Article
• Acceptance Date: Aug 30, 2022
• Online Publication Date: Oct 11, 2022
• Publication Date: 2022
• Deposit Date: Oct 7, 2022
• Publicly Available Date: Oct 7, 2022
• Journal: SciPost Physics
• Print ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Article Number: 092(2022)
• DOI: https://doi.org/10.21468/scipostphys.13.4.092