Mass Generation, Ghost Condensation and Broken Symmetry: SU(2) in Covariant Abelian Gauges

TL;DR

This paper explores how ghost condensation in SU(2) gauge theories within covariant Abelian gauges leads to spontaneous symmetry breaking, mass generation, and an Abelian Higgs mechanism, with implications for the theory's renormalizability.

Contribution

It demonstrates the spontaneous breaking of a global SL(2,R) symmetry via ghost condensation and interprets the resulting massless BRST quartets as an Abelian Higgs mechanism.

Findings

Ghost-antighost condensation occurs at small coupling.

Propagators are finite at Euclidean momenta except for the photon.

The symmetry breaking produces massless BRST quartets, indicating an Abelian Higgs mechanism.

Abstract

The local action of an SU(2) gauge theory in general covariant Abelian gauges and the associated equivariant BRST symmetry that guarantees the perturbative renormalizability of the model are given. A global SL(2,R) symmetry of the model is spontaneously broken by ghost-antighost condensation at arbitrarily small coupling. This leads to propagators that are finite at Euclidean momenta for all elementary fields except the Abelian ``photon''. Ward Identities show that the symmetry breaking gives rise to massless BRST-quartets with ghost numbers (1,2,-2,-1) and (0,1,-1,0). The latter quartet is interpreted as due to an Abelian Higgs mechanism in the dual description of the model.