Understanding the Strong Coupling Limit of the ${\cal N}=4$ Supersymmetric Yang-Mills at Finite Temperature

TL;DR

This paper explains how strongly coupled ${ m N}=4$ supersymmetric Yang-Mills theory exhibits a constant density of light bound states and coupling-independent thermodynamics, using gauge theory insights and the AdS/CFT correspondence.

Contribution

It provides a physical picture of strong coupling effects, including a modified Coulomb law and the formation of light bound states, connecting gauge theory results with the AdS/CFT correspondence.

Findings

Constant density of light bound states at all coupling strengths

Coupling-independent thermodynamics and kinetics at strong coupling

Qualitative agreement with known strong coupling screening results

Abstract

Recently, a number of intriguing results have been obtained for strongly coupled ${\cal N}=4$ Supersymmetric Yang-Mills theory in vacuum and matter, using the AdS/CFT correspondence. In this work, we provide a physical picture supporting and explaining most of these results within the gauge theory. The modified Coulomb's law at strong coupling forces static charges to communicate via the high frequency modes of the gauge/scalar fields. Therefore, the interaction between even relativistically moving charges can be approximated by a potential. At strong coupling, WKB arguments yield a series of deeply bound states, whereby the large Coulomb attraction is balanced by centrifugation. The result is a constant density of light bound states at {\bf any} value of the strong coupling, explaining why the thermodynamics and kinetics are coupling constant independent. In essence, at strong coupling the matter is not made of the original quasiparticles but of much lighter (binary) composites. A transition from weak to strong coupling is reminiscent to a transition from high to low $T$ in QCD. We establish novel results for screening in vacuum and matter through a dominant set of diagrams some of which are in qualitative agreement with known strong coupling results.