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

Yoshimasa Hidaka and Robert D. Pisarski

Arxiv ID: 0906.1751•Last updated: 9/4/2020

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.

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