Transport equation and hard thermal loops in noncommutative Yang-Mills theory

TL;DR

This paper demonstrates that the high-temperature behavior of noncommutative thermal Yang-Mills theory can be derived from the Boltzmann transport equation, simplifying the calculation of gluon functions and constructing the hard thermal loop effective action.

Contribution

It introduces a straightforward Boltzmann approach to derive high-temperature limits and constructs the HTL effective action in noncommutative Yang-Mills theory.

Findings

Gluon functions are gauge invariant and satisfy Ward identities.

High-temperature limit obtained from classical particle transport.

Constructed the HTL effective action for noncommutative theory.

Abstract

We show that the high temperature limit of the noncommutative thermal Yang-Mills theory can be directly obtained from the Boltzmann transport equation of classical particles. As an illustration of the simplicity of the Boltzmann method, we evaluate the two and the three-point gluon functions in the noncommutative U(N) theory at high temperatures T. These amplitudes are gauge invariant and satisfy simple Ward identities. Using the constraint satisfied at order T^2 by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory.