Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections

Abstract

We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in N=4 super Yang-Mills theory in the totally antisymmetric representation of the gauge group U(N) or SU(N). Localization and matrix model techniques provide exact, but rather formal, expressions for these expectation values. In this paper we show how to extract the leading and sub-leading behavior in a 1/N expansion with fixed 't Hooft coupling starting from these exact results. This is done by exploiting the relation between the generating function of antisymmetric Wilson loops and a finite-dimensional quantum system known as the truncated harmonic oscillator. Sum and integral representations for the 1/N terms are provided.

arXiv comment32 pages, 2 figures, v2: added references

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Cited by in corpus (7)

• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Wilson loops in terms of color invariants
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $\mathcal{N}=4$ SYM theory
• Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
• Exact 1/N expansion of Wilson loop correlators in $\mathcal{N}=4$ Super-Yang-Mills theory