Exploring quark-gluon plasma on the loop space

TL;DR

This paper reformulates the Langevin equation for soft modes in quark-gluon plasma on loop space, solving the loop equation under specific gauge conditions and discussing perturbation theory in terms of the 't Hooft coupling.

Contribution

It introduces a novel loop space formulation of the Langevin equation and provides solutions and perturbative analysis for the loop equations in quark-gluon plasma.

Findings

Solved the loop equation for specific gauge potentials.

Derived a regularized form of the loop equation.

Discussed perturbation theory in the 't Hooft coupling.

Abstract

Langevin equation describing soft modes in the quark-gluon plasma is reformulated on the loop space. The Cauchy problem for the resulting loop equation is solved for the case when the nonvanishing components of the gauge potential correspond to the Cartan generators of the SU(N)-group and are proportional to a constant unit vector in the Cartan subalgebra. The regularized form of the loop equation with an arbitrary gauge potential is found, and perturbation theory in powers of the 't Hooft coupling is discussed.