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

TL;DR

<3-5 sentence high-level summary>This paper leverages the gauge/gravity correspondence to study confinement, Wilson loops, and phase structure of large $N$ gauge theories across dimensions by analyzing extremal and near-extremal D-brane backgrounds. Using the Nambu-Goto action and holographic thermodynamics, it demonstrates area-law behavior for spatial Wilson loops in non-supersymmetric theories derived from compactifications and shows no first-order finite-temperature phase transitions between SYM and SUGRA regimes for theories with maximal supersymmetry, with entropy matching across regimes. The results connect confinement diagnostics in lower-dimensional theories to higher-dimensional origin, and reveal a consistent, crossover-like evolution between weakly coupled gauge theories and gravity duals, rather than sharp transitions, across multiple $p$-brane backgrounds. These findings strengthen the holographic picture of confinement and clarify the thermodynamic interplay between gauge theories and their gravitational duals in the large $N$ limit, including finite-temperature effects and quark-antiquark potentials.

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.