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Dyson equations for correlators of Wilson loops. (English) Zbl 1405.81150
Summary: 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.

MSC:
81T60 Supersymmetric field theories in quantum mechanics
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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