Effective Polyakov line action from the relative weights method

TL;DR

This paper derives an effective Polyakov line action for SU(2) lattice gauge theory using the relative weights method, demonstrating its accuracy through correlator comparisons with the original lattice theory.

Contribution

The paper applies the relative weights method to explicitly determine a bilinear effective Polyakov line action for SU(2) gauge theory in the confined phase.

Findings

Effective action is bilinear in Polyakov lines.

Finite range kernel has a simple expression.

Polyakov line correlators agree closely between effective and original theories.

Abstract

We apply the relative weights method (arXiv:1209.5697) to determine the effective Polyakov line action for SU(2) lattice gauge theory in the confined phase, at lattice coupling beta=2.2 and N_t=4 lattice spacings in the time direction. The effective action turns out to be bilinear in the fundamental representation Polyakov line variables, with a rather simple expression for the finite range kernel. The validity of this action is tested by computing Polyakov line correlators, via Monte Carlo simulation, in both the effective action and the underlying lattice theory. It is found that the correlators in each theory are in very close agreement.