Spacelike strings and jet quenching from a Wilson loop

TL;DR

This paper explores spacelike string solutions in AdS black hole backgrounds to evaluate the jet quenching parameter in N=4 SYM, revealing that the proposed non-perturbative definition yields zero, with the dominant solution showing linear dependence on quark separation.

Contribution

It demonstrates that the non-perturbative Wilson loop definition results in a zero jet quenching parameter and analyzes the behavior of spacelike string solutions in this context.

Findings

The jet quenching parameter is zero under the non-perturbative definition.

The dominant string solution exhibits linear dependence on quark separation.

Multiple branches of spacelike solutions exist in the AdS black hole background.

Abstract

We investigate stationary string solutions with spacelike worldsheet in a five-dimensional AdS black hole background, and find that there are many branches of such solutions. Using a non-perturbative definition of the jet quenching parameter proposed by Liu et. al., hep-ph/0605178, we take the lightlike limit of these solutions to evaluate the jet quenching parameter in an N=4 super Yang-Mills thermal bath. We show that this proposed definition gives zero jet quenching parameter, independent of how the lightlike limit is taken. In particular, the minimum-action solution giving the dominant contribution to the Wilson loop has a leading behavior that is linear, rather than quadratic, in the quark separation.