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arXiv · 2102.08305

A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory

Daniele Dorigoni·Michael B. Green·Congkao Wen
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Abstract

An integrated correlator of four superconformal stress-tensor primaries of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory (SYM), originally obtained by localisation, is re-expressed as a two-dimensional lattice sum that is manifestly invariant under $SL(2,\mathbb{Z})$ S-duality. This expression is shown to satisfy a novel Laplace equation in the complex coupling constant $τ$ that relates the $SU(N)$ integrated correlator to those of the $SU(N+1)$ and $SU(N-1)$ theories. The lattice sum is shown to precisely reproduce known perturbative and non-perturbative properties of $\mathcal{N}=4$ SYM for any finite $N$, as well as extending previously conjectured properties of the large-$N$ expansion.

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Daniele Dorigoni, Michael B. Green, Congkao Wen. 2021-04-26. A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory. https://doi.org/10.1103/physrevlett.126.161601

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