The finite 't Hooft coupling correction on the jet quenching parameter in a $\mathcal N=4$ Super Yang-Mills Plasma

TL;DR

This paper calculates the first correction to the jet quenching parameter in a strongly coupled $ ext{AdS}_5$-Schwarzschild background, revealing that quantum fluctuations decrease the parameter at finite 't Hooft coupling.

Contribution

It provides the first explicit computation of the finite 't Hooft coupling correction to the jet quenching parameter in $ ext{AdS}_5$-Schwarzschild, including numerical evaluation of fluctuation determinants.

Findings

Jet quenching parameter decreases due to world sheet fluctuations.

Correction factor is approximately $(1 - 1.97 imes ext{lambda}^{-1/2})$.

Results are relevant for understanding finite coupling effects in holographic QCD.

Abstract

We derive the quadratic action of the fluctuations around the classical world sheet underlying the jet quenching from AdS/CFT. After obtaining the correspondence partition function, the expansion of the jet quenching parameter of $\mathcal N=4$ super symmetric Yang-Mills theory is carried out to the sub-leading term in the large 't Hooft coupling $\lambda$ at a nonzero temperature. The strong coupling corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The contribution of these determinants are evaluated numerically. We find the jet quenching parameter is reduced due to world sheet fluctuations by a factor $(1-1.97\lambda^{-1/2}) $