Wilson loops beyond the planar limit in the ADS/CFT correspondence.
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Date
2019
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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.
Description
Tesis (Magíster en Física)--Pontificia Universidad Católica de Chile, 2019