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

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.

Comments: 52 pages, 10 figures; Eqs. (118), (137), and (158) have been corrected. We thank H. Nishimura and V. V. Skokov for pointing this out