Two-dimensional gluon propagators in maximally Abelian gauge in SU(2) Lattice QCD

TL;DR

This study investigates two-dimensional SU(2) lattice QCD in the maximally Abelian gauge, revealing the effects of Gribov copies and the absence of Abelian dominance, with detailed analysis of gluon propagators in momentum and coordinate space.

Contribution

The paper provides the first detailed lattice QCD analysis of diagonal and off-diagonal gluon propagators in 2D MAG, highlighting Gribov copy effects and the lack of Abelian dominance.

Findings

Diagonal gluon propagator suppressed in infrared with increasing β

Spectral functions of gluons show negative regions, violating Kallen-Lehmann representation

No evidence of Abelian dominance in two-dimensional SU(2) lattice QCD

Abstract

Using SU(2) lattice QCD in two dimensions, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge (MAG) with U(1)$_3$ Landau gauge fixing. These propagators are investigated both in momentum space and coordinate space. The Monte Carlo simulation is performed at $\beta=7.99, 30.5,$ and $120$ on $62^2, 128^2,$ and $256^2$ at the quenched level. In the momentum space, the transverse component of the diagonal gluon propagator shows suppression with increasing $\beta$ in the infrared region and the dressing function at $\beta=120$ has a maximum at $p^2 \simeq 4$GeV, while the transverse component of the off-diagonal gluon propagator does not show the $\beta$-dependence and the dressing function does not have a maximum. This behavior indicates that the effect of the Gribov copies is found for the diagonal gluon, consistent with the result obtained by the Gribov-Zwanziger action in the MAG. In addition, this behavior supports that the Abelian dominance is not found in two dimensions. In the coordinate space, the diagonal gluon propagator decreases as $\beta$ increases at long distance. In particular, at $\beta=120$ the diagonal propagator decreases more rapidly with increasing distance than the off-diagonal propagator. These behaviors also indicate the presence of Gribov copies and no Abelian dominance in two dimensions. Furthermore, we also study these propagators at zero-spatial-momentum. The result suggests that all of the spectral functions of diagonal and off-diagonal gluons would have negative regions and thus they show the violation of the Kallen-Lehmann representation.