Abstract
We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in mathcal{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.
Highlights
A key ingredient in the description of Wilson loop operators is the representation of the gauge group, typical ones for U(N ) and SU(N ) being the fundamental, totally symmetric and totally antisymmetric representations
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
We address and solve the problem of extracting the leading and first subleading terms in the 1/N expansion of the generating function of totally antisymmetric Wilson loops starting from the exact results in [48]
Summary
We begin this section by reviewing this model and developing some results that will be relevant for what follows
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