On the infrared behavior of Green's functions in Yang-Mills theory

Abstract

Non-perturbative properties of QCD, such as color confinement, are encoded in the infrared behavior of correlation functions, e.g. propagators and vertices. Various analytic predictions have been suggested for these quantities in various gauges. Here we numerically test these predictions using lattice gauge theory. In particular, we present results for the 2-and 3-point functions for SU(2) Landau-gauge Yang-Mills theory in three and in four dimensions. Special attention is paid to systematic finite-volume effects. The gluon and ghost propagators are also evaluated in the so-called interpolating gauge (between the Landau and the Coulomb gauge), in order to study their gauge-dependence. Finally, we consider these propagators in Landau gauge at finite temperature, with the aim of understanding the effect of the deconfinement phase transition on their infrared behavior. All our results are compatible with the so-called Gribov-Zwanziger confinement scenario.

Infrared behavior of the gluon and ghost propagators in Yang-Mills theories

“…It induces an infrared suppressed gluon propagator, a fact in qualitative agreement with lattice [29] and Schwinger-Dyson results [30,31,32]. Let us also mention that (3.16) violates spectral positivity, giving an indication that the gauge bosons are unphysical particles [26] …”

“…Using the gap equation arising from the horizon condition, one finds that [3,22,23,25,26,27] This enhancement remains valid in the presence of A 2 [25,26]. The infrared enhancement of the ghost propagator in the Landau gauge has also been observed from lattice simulations [29,28] or solutions of the Schwinger-Dyson equations [30,31,32]. The Gribov restriction and A 2 also affect the gluon propagator in a nontrivial fashion, more precisely one finds [25,26] …”

Erratum: Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator [Phys. Rev. D77, 014504 (2008)]

“…[8]). So far, only in two and three dimensions it was possible to reach the expected asymptotics in an unambigious manner [9,10,11]. In four dimensions, for SU (2) as well as SU (3) lattice gauge theory, the ultimate decrease of the gluon propagator towards vanishing momentum has not yet been established.…”

Just how different are theSU(2)andSU(3)Landau-gauge propagators in the infrared regime?

“…pure SU (3) Yang-Mills theory] [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], in pure SU (2) Yang-Mills theory (in 2, 3 and 4 space-time dimensions) [31,32,33,34,35,36,37,38,39,40,41] and in full QCD [42,43,44,45]. All lattice studies in 4d suggest a finite nonzero infrared gluon propagator [20,24,26,27,42], in contradiction with the infrared Schwinger-Dyson solution.…”

“…The corresponding β values for SU (2) were computed using the asymptotic scaling analysis discussed in [35]. propagator G(k 2 ) has been studied in [22,25,28,29,30,31,38,39,40,41,43,47,48,49,50,51,52,53] and in all cases an enhancement of the propagator compared to the tree-level behavior 1/k 2 was observed. Concerning the comparison between lattice results and the SDE solution, the two propagators seem to agree only qualitatively.…”