Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop

TL;DR

This paper calculates quadratic order hard thermal loops in a SU(N) gauge theory with a spatial 't Hooft loop background, providing insights into transport properties of a semi-Quark Gluon Plasma.

Contribution

It develops a general technique to compute hard thermal loops in the presence of a background field, extending previous methods to include quadratic order effects and finite N analysis.

Findings

Quark self-energy has a Q-dependent thermal mass squared of order g^2T^2.

Gluon self-energy includes a Q-dependent Debye mass squared and a new hard thermal loop of order g^2T^3.

Techniques can be applied to study transport properties in semi-Quark Gluon Plasma.

Abstract

We compute the simplest hard thermal loops for a spatial 't Hooft loop in the deconfined phase of a SU(N) gauge theory. We expand to quadratic order about a constant background field A_0 = Q/g, where Q is a diagonal, color matrix and g is the gauge coupling constant. We analyze the problem in sufficient generality that the techniques developed can be applied to compute transport properties in a "semi"-Quark Gluon Plasma. Notably, computations are done using the double line notation at finite N. The quark self-energy is a Q-dependent thermal mass squared, of order g^2T^2, where T is the temperature, times the same hard thermal loop as at Q=0. The gluon self-energy involves two pieces: a Q-dependent Debye mass squared, of order g^2T^2, times the same hard thermal loop as for Q=0, plus a new hard thermal loop, of order g^2T^3, due to the color electric field generated by a spatial 't Hooft loop.