Dyson equations for correlators of Wilson loops

Abstract

By considering a Gaussian truncation of $\mathcal{N}=4$ super Yang-Mills, we derive a set of Dyson equations that account for the ladder diagram contribution to connected correlators of circular Wilson loops. We consider different numbers of loops, with different relative orientations. We show that the Dyson equations admit a spectral representation in terms of eigenfunctions of a Schrödinger problem, whose classical limit describes the strong coupling limit of the ladder resummation. We also verify that in supersymmetric cases the exact solution to the Dyson equations reproduces known matrix model results.

arXiv comment36 pages, 10 figures; v2 references, minor corrections and clarifications added; published version

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Cited by in corpus (7)

• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• More on Wilson loops for two touching circles
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops