Propagators and Dimensional Reduction of Hot SU(2) Gauge Theory

TL;DR

This study compares the electric and magnetic propagators of hot SU(2) gauge theory in 4d and 3d lattice simulations, showing dimensional reduction is effective down to twice the critical temperature and revealing gauge-dependent features in magnetic propagators.

Contribution

It demonstrates the validity of dimensional reduction for hot SU(2) gauge theory at relatively low temperatures and analyzes gauge dependence of magnetic propagators.

Findings

Dimensional reduction works well down to T=2 T_c.

Electric screening mass is gauge independent.

Magnetic propagator shows gauge-dependent structure at low momentum.

Abstract

We investigate the large distance behavior of the electric and magnetic propagators of hot SU(2) gauge theory in different gauges using lattice simulations of the full 4d theory and the effective, dimensionally reduced 3d theory. Comparison of the 3d and 4d propagators suggests that dimensional reduction works surprisingly well down to the temperature T=2 T_c. Within statistical uncertainty the electric screening mass is found to be gauge independent. The magnetic propagator, on the other hand, exhibits a complicated gauge dependent structure at low momentum.