Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

TL;DR

This paper derives an effective monopole action at finite temperature in SU(2) gluodynamics, showing temperature-dependent spacelike monopole couplings and confirming dimensional reduction to a 3D model at high temperatures.

Contribution

It introduces a method to determine the 4D effective monopole action at finite temperature and demonstrates its agreement with the reduced 3D model at high temperatures.

Findings

Effective monopole action depends on temperature and physical scale.

Spacelike monopole couplings vary with temperature in the deconfinement phase.

Dimensional reduction to the 3D Georgi-Glashow model is validated at high temperature.

Abstract

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.