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We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of N=4 𝒩 = 4 supersymmetric Yang–Mills (SYM) theory with classical gauge group, GN G N = SO (2N) = S O (2 N), SO (2N+1) S O (2 N + 1), USp (2N) U S p (2 N). 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) S U (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 =/ (2) + 4 i /g²_ₘ₌ τ = θ / (2 π) + 4 π i / g Y M 2 on any integrated correlator for gauge group GN G N relates it to a linear combination of correlators with gauge groups G₍+₁ G N + 1, GN G N and G₍-₁ G N − 1. These ``Laplace-difference equations’’ determine the expressions of integrated correlators for all classical gauge groups for any value of <jats: alternat
Dorigoni et al. (Tue,) studied this question.