Wilson loops beyond the planar limit in the ADS/CFT correspondence.

Abstract

Motivated by the AdS/CFT correspondence, the vacuum expectation values of 1/2-BPS circular Wilson loops in N = 4 super Yang-Mills theory are considered. Localization and matrix model techniques provide exact, but rather formal, expressions for these expectation values. In this thesis, the leading and sub-leading behavior in a 1/N expansion with fixed ’t Hooft coupling, and then in the holographic regime, are extracted 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. The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group U(N) are expressed in terms of the connected correlators of multiply-wound Wilson loops, which have a 1/N2 genus expansion, using ingredients from the representation theory of the symmetric group. Interesting conclusions on the gravity side of the correspondence are provided.