On the exact solution of the accelerating string in $AdS_5$ space

TL;DR

This paper derives an exact accelerating string solution in AdS_5 space, revealing a scale that separates radiation from the heavy quark, and establishes a new link between the AdS horizon and Unruh temperature, with calculations of momentum broadening.

Contribution

It presents an exact solution for accelerating strings in AdS_5 and uncovers a novel correspondence between the AdS horizon and Unruh temperature, advancing understanding of quark radiation in holography.

Findings

Identified a scale acting as an event horizon in the string's proper frame.

Established a new correspondence between the AdS horizon and Unruh temperature.

Computed momentum broadening of heavy quarks due to radiation.

Abstract

In this letter, the exact accelerating string solution of a heavy quark-antiquark pair is found in $AdS_5$ space. On the accelerating string, there is a particular scale which separates the radiation and the heavy quark. This scale is explicitly shown to be an event horizon in the proper frame of the heavy quark. Furthermore, we find a new correspondence, which relates the horizon in $AdS_5$ space on the gravity theory side to the Unruh temperature in Minkowski space on the field theory side of the AdS/CFT correspondence. $p_{\perp}$-broadening and $p_{L}$-broadening of the heavy quark due to radiation are computed using the AdS/CFT correspondence.