Temporal correlator in YM^2_3 and reflection-positivity violation

TL;DR

This study analyzes the lattice Landau gluon propagator in 3D SU(2) Yang-Mills theory, revealing oscillatory behavior and reflection-positivity violation, which are linked to gluon confinement, supported by fitting with Stingl-like propagators.

Contribution

It provides numerical evidence of reflection-positivity violation in the gluon propagator and models it with Stingl-like propagators in three-dimensional Yang-Mills theory.

Findings

Temporal correlator C(t) is oscillatory and negative.

Reflection positivity is explicitly violated.

Fitting with Stingl-like propagators describes the data well.

Abstract

We consider numerical data for the lattice Landau gluon propagator obtained at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge theory (YM^2_3). We find that the temporal correlator C(t) shows an oscillatory pattern and is negative for several values of t. This is an explicit violation of reflection positivity and can be related to gluon confinement. We also obtain a good fit for this quantity in the whole time interval using a sum of Stingl-like propagators.