High-temperature limit of Landau-gauge Yang-Mills theory

Abstract

Abstract. The infrared properties of the high-temperature limit of Landau-gauge Yang-Mills theory are investigated. In a first step the high-temperature limit of the Dyson-Schwinger equations is taken. The resulting equations are identical to the Dyson-Schwinger equations of the dimensionally reduced theory, a three-dimensional Yang-Mills theory coupled to an effective adjoint Higgs field. These equations are solved analytically in the infrared and ultraviolet, and numerically for all Euclidean momenta. We find infrared enhancement for the Faddeev-Popov ghosts, infrared suppression for transverse gluons and a mass for the Higgs. These results imply long-range interactions and over-screening in the chromomagnetic sector of high temperature Yang-Mills theory while in the chromoelectric sector only screening is observed.

Solving a set of truncated Dyson–Schwinger equations with a globally converging method

“…The Higgs propagator is dominated by the renormalized mass term in equation (10) and thus has the unique exponent e H = −1. This also determines A H uniquely [8]. There are two possible solutions for the ghost exponents.…”

“…For physical reasons the choice of Landau gauge is advantageous, which will be made here exclusively. The Lagrangian of this system in Euclidean space is then given by [8,13] …”

“…Furthermore this induces an additional non-trivial dependence of M T on G and Z, see appendix A and ref. [8].…”

“…Therefore the infrared asymptotic behavior is of special interest. Favorable, it turns out that the leading asymptotic behavior can be obtained analytically [7,8,20].…”

“…One of the solution is e G = 1/2, while the other depends on ζ and varies as e G ∈ (1/4, 1/2]. The gluon exponent e Z is not independent, but related to e G by [8,20] …”