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.

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