Infrared Behavior of the Ghost Propagator in the Landau Gauge Yang-Mills Theory (original) (raw)
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Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories
Physical Review D, 2008
We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau-gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two dimensional case, on the other hand, we find that G(p) diverges as p^{-2-2 kappa} with kappa \approx 0.15, in agreement with Ref. [1]. We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Most of our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.
Infrared behavior of the gluon and ghost propagators in Yang-Mills theories
Arxiv preprint hep-th/ …, 2006
We provide a short discussion of the dimension two condensate A 2 and its influence on the infrared behaviour of the gluon propagator in the Landau gauge. Simultaneously, we pay attention to the issue of Gribov copies in the Landau gauge. We also briefly discuss a local, gauge invariant non-Abelian action with mass parameter, constructed from the dimension 2 operator F µν (D 2 ) −1 F µν .
Physical Review D, 2012
We study general properties of the Landau-gauge Gribov ghost form-factor σ(p 2) for SU(Nc) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p 2) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function σ(p 2) blows up in the infrared limit p → 0 as −D(0) ln(p 2). Thus, for d = 2, the no-pole condition σ(p 2) < 1 (for p 2 > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, σ(p 2) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p 2) explicitly at one loop, using fitting forms for D(p 2) that describe well the numerical data of the gluon propagator in two, three and four spacetime dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g 2 as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labelled by g 2), in agreement with previous works by Boucaud et al. In this case the condition σ(0) ≤ 1 implies g 2 ≤ g 2 c , where g 2 c is a "critical" value. Moreover, a free-like ghost propagator in the infrared limit is obtained for any value of g 2 smaller than g 2 c , while for g 2 = g 2 c one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for σ(p 2) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form-factor σ(p 2). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon, i.e. the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.
Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum
Nuclear Physics B - Proceedings Supplements, 2006
In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU (3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta q 2 ≤ 0.3 GeV 2 we find the corresponding MOM scheme running coupling αs(q 2 ) to rise in q. We also report on a first SU (3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.
On the IR behaviour of the Landau-gauge ghost propagator
Journal of High Energy Physics, 2008
We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.
Infrared finite ghost propagator in the Feynman gauge
Physical Review D, 2008
We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the non-perturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes non-trivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined.
Spectral decomposition of the ghost propagator and a necessary condition for confinement
Physical Review D, 2016
In this article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zero-modes of the Faddeev-Popov (FP) operator M (gA) = −∂ • D(gA). This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator G(k;gA) = k|M −1 (gA)| k in an external gauge potential A is enhanced at low k in Fourier space for configurations A on the Gribov horizon. This results from the new formula in the low-k regime G ab (k, gA) = δ ab λ −1 | k| (gA), where λ | k| (gA) is the eigenvalue of the FP operator that emerges from λ | k| (0) = k 2 at A = 0. Next we derive a strict inequality signaling the divergence of the color-Coulomb potential at low momentum k namely, V (k) ≥ k 2 G 2 (k) for k → 0, where V (k) is the Fourier transform of the color-Coulomb potential V (r) and G(k) is the ghost propagator in momentum space. Although the color-Coulomb potential is a gauge-dependent quantity, we recall that it is bounded below by the gauge-invariant Wilson potential, and thus its long range provides a necessary condition for confinement. The first result holds in the Landau and Coulomb gauges, whereas the second holds in the Coulomb gauge only.
Color confinement and the Faddeev-Popov ghosts in Coulomb gauge QCD
We investigate the Gribov-Zwanziger scenario in the Coulomb gauge using a SU(3) quenched lattice gauge simulation. The dressing function of the ghost propagator diverges in the infrared limit. This result is expected from the fact that the Faddeev-Popov eigenvalue density gets concentrated near the vanishing eigenvalue compared to that in the abelian gauge theory. The turnover of the transversal gluon propagator is not observed up to the largest lattice volume explored in this study. The instantaneous part of the time-time component of the gluon propagator which corresponds to the color-Coulomb potential in the continuum limit diverges stronger than the simple pole. Furthermore, we observe that the ghost propagator show good scaling while both components of the gluon propagator do not show scaling in the considered range of the lattice spacing.
The gluon and ghost propagator and the influence of Gribov copies
Nuclear Physics B - Proceedings Supplements, 2005
The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU (3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approach.
Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
Physical Review Letters, 1997
A solvable systematic truncation scheme for the Dyson-Schwinger equations of Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor identities for the three-gluon and ghost-gluon vertices, whereas irreducible four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering kernels are neglected. The infrared behavior of gluon and ghost propagators is obtained analytically: The gluon propagator vanishes for small spacelike momenta whereas the ghost propagator diverges more strongly than a massless particle pole. The numerical solutions are compared with recent lattice data for these propagators. The running coupling of the renormalization scheme approaches a fixed point, αc ≃ 9.5, in the infrared.