Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities

TL;DR

This paper investigates gluon scattering amplitudes in finite temperature gauge/gravity dualities, revealing how chemical potential and non-commutativity influence the minimal surfaces and amplitudes, with specific bounds and behaviors at different limits.

Contribution

It provides a detailed analysis of gluon scattering amplitudes at finite temperature with R-charge and non-commutative parameters, including the effects on minimal surfaces and amplitude bounds.

Findings

Amplitude decreases with increasing chemical potential or non-commutative parameter.

Short side length of Wilson loop has an upper bound depending on temperature and parameters.

Approach breaks down at zero temperature due to bounds going to zero.

Abstract

We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.