What does the string/gauge correspondence teach us about Wilson loops?

TL;DR

This paper reviews how the string/gauge correspondence helps compute Wilson loop expectation values across various backgrounds, including confining theories, finite temperature, and quantum corrections, highlighting new theoretical insights and conditions for confinement.

Contribution

It introduces a theorem for classical Wilson loop values in generalized backgrounds and explores quantum fluctuations beyond the classical string approximation.

Findings

Derived conditions for confining behavior in string models.

Extended Wilson loop calculations to finite temperature and non-trivial backgrounds.

Analyzed quantum fluctuations and their impact on Wilson loop values.

Abstract

In these lectures we describe the attempt to extract the expectation values of Wilson loops from the string/gauge correspondence. We start with the original calculation in $AdS_5$. It is then extended to the non-conformal background of $D_p$ in the near horizon limit. We discuss the computation at finite temperature. Supergravity models that admit confinement in 3d and 4d are described. A theorem that determines the classical values of loops associated with a generalized background is derived.In particular we determine sufficient conditions for confining behavior. We then apply the theorem to various string models including type 0 ones. We describe an attempt to go beyond the classical string picture by incorporating quadratic quantum fluctuations. In particular we address the BPS configuration of a single quark, the supersymmetric determinant of $AdS_5\times S^$ and a setup that corresponds to a confining gauge theory. We determine the form of the Wilson loop for actions that include non trivial $B_{\mu\nu}$ field. The issue of an exact determination of the value of the stringy Wilson loop is discussed. We end with a brief review of the baryons from the string/gauge correspondence Lectures presented in the ``Advanced School on Supersymmetry in the theories of fields, strings and branes'' Santiago de Compostela-99.