Infinite volume and continuum limits for gluon propagator in 3d SU(2) lattice gauge theory

TL;DR

This paper investigates the behavior of the gluon propagator in 3d SU(2) lattice gauge theory, demonstrating differences between regions in the infrared limit that persist in the continuum limit.

Contribution

It provides new insights into the infrared properties of the gluon propagator, highlighting differences between the Gribov and fundamental modular regions in the continuum limit.

Findings

Infrared differences between Gribov and fundamental regions

Results hold as lattice spacing approaches zero

Infrared behavior persists in the continuum limit

Abstract

We study the Landau gauge gluon propagator D(p) in the 3d SU(2) lattice gauge theory. We show that in the infinite-volume limit the expectation values over the Gribov region \Omega, are different (in the infrared) from that calculated in the fundamental modular region \Gamma. Also we show that this conclusion does not change when spacing $a$ tends to zero.