Two-dimensional gluon propagators in maximally Abelian gauge in 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.

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Cited by in corpus (2)

• Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge
• Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sector