Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group

Abstract

Recently, some reformulations of the Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition have been developed in order to understand confinement from the viewpoint of the dual superconductivity. In this paper we focus on the reformulated $SU(N)$ Yang-Mills theory in the minimal option with $U(N-1)$ stability group. Despite existing numerical simulations on the lattice we perform the perturbative analysis to one-loop level as a first step towards the non-perturbative analytical treatment. First, we give the Feynman rules and calculate all renormalization factors to obtain the standard renormalization group functions to one-loop level in light of the renormalizability of this theory. Then we introduce a mixed gluon ghost composite operator of mass dimension two and show the BRST invariance and the multiplicative renormalizability. Armed with these results, we argue the existence of the mixed gluon-ghost condensate by means of the so-called local composite operator formalism, which leads to various interesting implications for confinement as shown in preceding works.

arXiv commentIn the latest version, we corrected a previously wrong result for the anomalous dimension of the residual ghosts

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Cited by in corpus (3)

• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
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• The gluon condensate in an effective SU(2) Yang-Mills theory