2022/02/11 by Daniele Dorigoni, Michael Green, Dorigoni, Daniele +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2202.05784
openalex publication_date 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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) 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_YM 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 equation" 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 AdS5× S5/ℤ2 background.