More on ghost condensation in Yang-Mills theory: BCS versus Overhauser effect and the breakdown of the Nakanishi-Ojima annex SL(2,R) symmetry

TL;DR

This paper investigates ghost condensates in Yang-Mills theory within the Curci-Ferrari gauge, exploring their role in dynamical symmetry breaking and comparing effects analogous to BCS and Overhauser phenomena, with special focus on the Landau gauge.

Contribution

It provides a combined analysis of multiple ghost condensates using algebraic renormalization, revealing their role in breaking the Nakanishi-Ojima SL(2,R) symmetry in Yang-Mills theory.

Findings

Ghost condensates induce dynamical symmetry breaking.

The analysis clarifies the role of BCS and Overhauser effects in gauge theories.

Special case of Landau gauge highlights unique symmetry properties.

Abstract

We analyze the ghost condensates <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}> in Yang-Mills theory in the Curci-Ferrari gauge. By combining the local composite operator formalism with the algebraic renormalization technique, we are able to give a simultaneous discussion of <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}>, which can be seen as playing the role of the BCS, respectively Overhauser effect in ordinary superconductivity. The Curci-Ferrari gauge exhibits a global continuous symmetry generated by the Nakanishi-Ojima (NO) algebra. This algebra includes, next to the (anti-)BRST transformation, a SL(2,R) subalgebra. We discuss the dynamical symmetry breaking of the NO algebra through these ghost condensates. Particular attention is paid to the Landau gauge, a special case of the Curci-Ferrari gauge.