Dimension two condensates in the Gribov-Zwanziger theory in the Coulomb gauge

Abstract

We investigate the dimension two condensate $<{\bar{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\bar{\omega }}_i^{ab}{\omega }_i^{ab}>$ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate $<{\bar{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\bar{\omega }}_i^{ab}{\omega }_i^{ab}>$ is plagued by a non-integrable IR divergence in 3D, while in 4D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter ${\gamma }^2$. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behaviour, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behaviour, a decoupling solution might emerge too.

8 pages, version accepted for publication as a Rapid Communication in Physical Review D

References in corpus (20)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Coulomb gauge gluon propagator and the Gribov formula
• Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
• Equation of State of Gluon Plasma from Local Action
• Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
• The Coulomb gauge ghost Dyson-Schwinger equation
• Two-Point Functions of Coulomb Gauge Yang-Mills Theory
• The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates
• Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
• The effects of Gribov copies in 2D gauge theories
• A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon
• Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge
• Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge
• Vertex functions of Coulomb gauge Yang--Mills theory
• Functional approaches to infrared Yang-Mills theory in the Coulomb gauge

Cited by in corpus (5)

• Aspects of the refined Gribov-Zwanziger action in linear covariant gauges
• Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory
• Exploring new horizons of the Gribov problem in Yang-Mills theories
• Hints of (de)confinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge
• Generalized Faddeev-Popov Method for a Deformed Supersymmetric Yang-Mills Theory