Gluon scattering in ${\cal N}=4$ Super Yang-Mills at finite temperature

TL;DR

This paper extends the AdS/CFT framework to compute gluon scattering amplitudes at finite temperature in ${ m ext{N}=4}$ Super Yang-Mills, revealing new relations between amplitudes, Wilson loops, and plasma properties at strong coupling.

Contribution

It introduces a novel finite temperature prescription for gluon scattering amplitudes in AdS/CFT, differing from the zero temperature case, and relates these amplitudes to plasma parameters.

Findings

Calculated gluon scattering amplitude at strong coupling for specific energy regimes.

Established a connection between Wilson loops and jet quenching parameter at finite T.

Linked gluon scattering amplitudes to the viscosity coefficient of the plasma.

Abstract

We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature $T$, defining the amplitude for gluon scattering in ${\cal N}=4$ Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike ''Wilson loop'' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric, thus at finite $T$ there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate the amplitude at strong coupling for forward scattering of a low energy gluon ($E<T$) off a high energy gluon ($E\gg T$) in both cut-off and generalized dimensional regularization. The generalized dimensional regularization is defined in string theory as an IR modified dimensional reduction. For this calculation, the corresponding usual Wilson loop is related to the jet quenching parameter of the finite temperature ${\cal N}=4$ SYM plasma, while the gluon scattering amplitude is related to the viscosity coefficient.