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

TL;DR

This paper addresses how a strongly coupled ${ m N}=4$ SYM plasma can exhibit a modified, almost instantaneous Coulomb interaction while remaining in a Coulomb phase at all couplings. By explicitly summing ladder diagrams via the Bethe-Salpeter equation and analyzing a WKB bound-state spectrum, the authors show that the static potential scales as $V(L)\sim -{ m const} imes {rac{\sqrt{\lambda}}{L}}$ with a Debye-like screening at finite temperature, and that a density of light bound composites remains coupling-independent. They interpret these results as the gauge-theory realization of AdS/CFT findings: the thermodynamics and kinetics are governed by light, binary composites rather than original quasiparticles, leading to a near-perfect liquid behavior with universal transport properties. The work also develops a detailed finite-temperature diagrammatic framework—screened ladders and hard thermal loops—that reproduces and clarifies the qualitative and quantitative features of strong-coupling screening and bound-state formation, with implications for QGP-like systems and strongly coupled plasmas.

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.

Figures (5)

• Figure 1: Two types of solutions describing the potential between two static charges (large dots) in the ordinary 4-d space (on the D3 brane). The string originating from them can either connect them (a) or not (b). In both cases the string is deflected by a background metric (the gravity force indicated by the arrow marked g) downward, along the 5-th coordinate. After the string touches the black hole horizon (b) a Debye screening of the interaction takes place.
• Figure 2: (a) The color structure of ladder diagrams in the large-$N_c$ limit: each square is a different color trace, bringing the factor $N_c$. The time goes vertically, and the planarity condition enforces strict time ordering, $s_1>s_2>s_3...$, $t_1>t_2>t_3...$. (b) Schematic representation of the Bethe-Salpeter equation (\ref{['eqn_BS']}) summing ladders.
• Figure 3: Examples of higher-order diagrams with an extra scalar/gluon connecting the ladder rungs.
• Figure 4: Distribution of the interaction vertices in space. The black circles are static charges.
• Figure 5: The WKB spectrum versus 'tHooft coupling constant $\lambda$. (a) levels with fixed n=0 and $l=1..15$, (b) levels with fixed $l=10$ and $n=0..5$.