Gribov ambiguity in gauge theories

Gribov ambiguity in gauge field theories is discussed and it is shown that such an ambiguity exists even for Abelian theories in covariant gauge at finite temperature. Both geometric and algebraic proofs are presented. In view of the importance of non-perturbative methods, some special gauges are given in which such ambiguities do not exist or are not relevant. The significance of these in the study of confinement in QCD is pointed out.     

Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets Gribov copies originate mainly from zero-momentum modes of the gauge fields. The removal of the zero-momentum modes is necessary for reaching the absolute maximum of the Lorentz gauge functional.     

Covariant quantization of gauge fields without Gribov ambiguity

Recently Parisi and Wu proposed a method of quantizing gauge fields whereby euclidean expectation values are obtained by relaxation to equilibrium of a stochastic process depending on an artificial fifth time parameter. In the present work the equilibrium distribution is determined directly, without reference to the artificial time, by a stationary condition which is an eigenfunction equation in the euclidean Hilbert space. The solution has a perturbative expansion which appears renormalizable by naive power counting. Because of gauge freedom, a free dimensionless gauge parameter appears in the theory although no gauge condition such as ? · A = 0 is imposed.     

On Gribov ambiguity in finite temperature Abelian gauge theory

It is shown that there is Gribov ambiguity in finite temperature Abelian gauge theory if the gauge theory is defined on the full gauge orbit space. This is demonstrated geometrically and by an explicit construction of solutions to the Gribov equation. Its effects on the evaluation of the temperature-dependent partition function are noted using the Faddeev-Popov procedure.     

Degenerate gauge conditions,generalized Gribov ambiguity and BRST symmetry

The BFV-BRST approach to gauge theories is considered. It is argued that the BRST-invariant boundary conditions ordinarily used do not maintain the necessary degeneracy in the gauge fixing. As a by-product of this discussion, the existence of a generalized Gribov-like ambiguity is suggested. This ambiguity is, however, shown to be just a particular BRST transformation.     

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4³ × 8 lattices), β = 5.8 (400 4³ × 10 lattices and 100 6³ × 12 lattices), and β = 6.0 (100 4³ × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.     

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit β=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^{2}\ll\varLambda_{\mathrm{QCD}}^{2}$ . In the strong-coupling limit, this same behavior is obtained for the larger values of a ² q ² (in units of the lattice spacing a), where it is otherwise swamped by the gauge-field dynamics. Deviations for a ² q ²<1 are well parameterized by a transverse gluon mass ∝1/a. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes (Phys. Rev. D 81:016005, 2010).     

Some remarks on the Gribov ambiguity

The set of all connections of a principal bundle over the 4-sphere with compact nonabelian Lie group under the action of the group of gauge transformations is studied. It is shown that no continuous choice of exactly one connection on each orbit can be made. Thus the Gribov ambiguity for the Coloumb gauge will occur in all other gauges. No gauge fixing is possible.     

On the Gribov ambiguity in the Faddeev-Popov procedure

The standard Faddeev-Popov procedure for quantization of a gauge theory is modified so as to be valid even when the Gribov problem is present. The hamiltonian is employed and a definite expression for the path integral is obtained for a wide class of gauges.     

Gribov horizon in the presence of dynamical mass generation in Euclidean Yang–Mills theories in the Landau gauge

We find the Goldstino action descending from the N=1 Goldstone–Maxwell superfield action associated with the spontaneous partial supersymmetry breaking, N=2 to N=1, in superspace. The new Goldstino action has higher (second-order) spacetime derivatives, while it can be most compactly described as a solution to the simple recursive relation. Our action seems to be related to the standard (having only the first-order derivatives) Akulov–Volkov action for Goldstino via a field redefinition.     

Every gauge orbit passes inside the Gribov horizon

TheL ² topology is introduced on the space of gauge connectionsA and a natural topology is introduced on the group of local gauge transformationsGT. It is shown that the mappingGT×AA defined byAA ^g=g^*Ag+g^*dg is continuous and that each gauge orbit is closed. The Hilbert norm of the gauge connection achieves its absolute minimum on each gauge orbit, at which point the orbit intersects the region bounded by the Gribov horizon.CNR, GNFMResearch supported in part by the National Science Foundation under grant no. PHY 87-15995     

A modification of Faddeev-Popov approach free from Gribov ambiguity

We propose a modified version of the Faddeev-Popov (FP) quantization approach for non-Abelian gauge field theory to avoid Gribov ambiguity. We show that by means of introducing a new method of inserting the correct identity into the Yang-Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of Gribov ambiguity can be removed naturally. Meanwhile by handling the absolute value of the FP determinant with the method introduced by Williams and collaborators, we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian. The new Lagrangian will have a nilpotent symmetry which can be viewed as an analog of the Becchi-Rouet-Stora-Tyutin symmetry.