The Diagonal Ghost Equation Ward Identity for Yang-Mills Theories in the Maximal Abelian Gauge

TL;DR

This paper introduces a new Ward identity in SU(N) Yang-Mills theories within maximal Abelian gauges, which helps control diagonal ghost dependence and ensures stability under radiative corrections, impacting the understanding of gauge coupling behavior.

Contribution

It presents the diagonal ghost equation, a novel renormalizable Ward identity that stabilizes the theory and relates the beta function to the vacuum polarization tensor.

Findings

Diagonal ghost equation controls ghost dependence.

Vanishing anomalous dimension of diagonal ghosts.

Beta function derived from vacuum polarization tensor.

Abstract

A BRST perturbative analysis of SU(N) Yang-Mills theory in a class of maximal Abelian gauges is presented. We point out the existence of a new nonintegrated renormalizable Ward identity which allows to control the dependence of the theory from the diagonal ghosts. This identity, called the diagonal ghost equation, plays a crucial role for the stability of the model under radiative corrections implying, in particular, the vanishing of the anomalous dimension of the diagonal ghosts. Moreover, the Ward identity corresponding to the Abelian Cartan subgroup is easily derived from the diagonal ghost equation. Finally, a simple proof of the fact that the beta function of the gauge coupling can be obtained from the vacuum polarization tensor with diagonal gauge fields as external legs is given. A possible mechanism for the decoupling of the diagonal ghosts at low energy is also suggested.