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

Abstract

We analyze the ghost condensates 〈fabccbc c〉, 〈fabcc-bc-c〉 and 〈fabcc-bcc〉 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 〈fabccbcc〉, 〈fabccbcc〉 and 〈f abccbcc〉, 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, Rdbl;) sub-algebra. 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. © SISSA/ISAS 2003.