Positivity violation for the lattice Landau gluon propagator

TL;DR

This paper provides numerical evidence of positivity violation in the lattice Landau gluon propagator, supporting the idea of gluon confinement in three-dimensional SU(2) gauge theory through large-volume lattice simulations.

Contribution

It presents the first detailed numerical analysis showing positivity violation for the Landau gluon propagator on large lattices in three dimensions.

Findings

Reflection-positivity violation observed in the gluon propagator.

Oscillatory pattern in the real-space propagator C(t).

Good scaling and fit with Gribov-like form in the data.

Abstract

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.