Wilson Loops, Confinement, and Phase Transitions in Large N Gauge Theories from Supergravity

TL;DR

This paper employs supergravity techniques to analyze Wilson loops and phase transitions in large N gauge theories, revealing confinement indications and the absence of certain phase transitions at finite temperature.

Contribution

It introduces a supergravity-based method to compute Wilson loops in various dimensions and analyzes phase transitions in supersymmetric gauge theories at finite temperature.

Findings

Spatial Wilson loops follow an area law in certain supersymmetric theories.

No phase transitions occur between weak and strong coupling regimes at finite temperature.

Entropy calculations show the absence of first-order phase transitions.

Abstract

We use the recently proposed supergravity approach to large $N$ gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.