On the internal space dependence of the static quark-antiquark potential in ${\cal N}=4$ SYM plasma wind

TL;DR

This paper investigates how the relative orientation of a quark-antiquark pair in the internal S^5 space affects their static potential and screening length in a strongly coupled ${ m N}=4$ SYM plasma, revealing orientation-dependent effects and proposing averaging for QCD relevance.

Contribution

It introduces the dependence of the static potential and screening length on the internal S^5-angle and suggests averaging over orientations to relate to QCD.

Findings

Velocity scaling law for screening length holds for all orientations.

Prefactor Z varies with the S^5-angle, affecting the potential.

Averaging Z over orientations suppresses the potential compared to aligned case.

Abstract

We study the effect of the relative S^5-angle of a quark and an antiquark on their static potential and the related screening length in a strongly coupled moving ${\cal N}=4$ SYM plasma. The large velocity scaling law for the screening length holds for any relative S^5-angle $\theta$. However, the velocity independent prefactor Z strongly depends on $\theta$. For comparison with QCD we propose to average Z over all relative orientations on S^5. This generates a suppression factor relative to the case $\theta =0$.