Effective Polyakov line action from strong lattice couplings to the deconfinement transition

TL;DR

This paper derives an effective Polyakov line action for SU(2) lattice gauge theory across a range of couplings, validating it through correlator comparisons and revealing its simple bilinear form and evolving interaction range.

Contribution

It introduces a method to compute the effective Polyakov line action from strong to deconfinement couplings, demonstrating its validity and simplicity across different regimes.

Findings

Effective action is bilinear in Polyakov lines.

Good agreement with gauge theory correlators for beta > 1.4.

Range of bilinear term increases with beta.

Abstract

We calculate the effective Polyakov line action corresponding to SU(2) lattice gauge theory on a 16^3 X 4 lattice via the "relative weights" method. We consider a variety of lattice couplings, ranging from beta=1.2 in the strong-coupling domain, to beta=2.3 at the deconfinement transition, in order to study how the effective action evolves with beta. Comparison of Polyakov line correlators computed in the effective theory and the underlying gauge theory is used to test the validity of the effective action for beta > 1.4, while for beta=1.2, 1.4 we can compare our effective action to the one obtained from a low-order strong-coupling expansion. Very good agreement is found at all couplings. We find that the effective action is given by a simple expression bilinear in the Polyakov lines. The range of the bilinear term, away from strong coupling, grows rapidly in lattice units as beta increases.