Stringy Confining Wilson Loops

TL;DR

This paper reviews how Wilson loops in confining gauge theories can be derived from their string duals, establishing classical conditions for confinement and analyzing quantum fluctuations in various models.

Contribution

It derives a theorem for classical Wilson loop values in generalized backgrounds and explores quantum effects in multiple confining models, highlighting the necessity of worldvolume phenomena.

Findings

Classical conditions for confining Wilson loops are established.

Quantum fluctuations produce an attractive Luscher term.

Worldvolume phenomena are essential for accurate modeling in certain theories.

Abstract

The extraction of Wilson loops of confining gauge systems from their SUGRA (string) duals is reviewed. I start with describing the basic classical setup. A theorem that determines the classical values of the loops associated with a generalized background is derived. In particular sufficient conditions for confining behavior are stated . I then introduce quadratic quantum fluctuations around the classical configurations. I discuss in details the following models of confining behavior: (i) Strings in flat space-time, (ii) $AdS_5$ black hole and its correspondence with pure YM theory in three dimensions. In particular an attractive Luscher term is shown to be the outcome of the quantum fluctuations. (iii) Type 0 string model (iv) The Polchinski Strassler $N=1*$ model. In the latter case we show that SUGRA alone is not enough to get the correct nature of the loops, and only by incorporating the worldvolume phenomena of the five branes a coherent qualitative picture can be derived.