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

TL;DR

This paper performs a one-loop perturbative analysis of the reformulated $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group, focusing on renormalization and the potential for gluon-ghost condensates related to confinement.

Contribution

It provides the first perturbative calculation of renormalization factors and explores the existence of gluon-ghost condensates in a reformulated Yang-Mills framework with $U(N-1)$ stability.

Findings

Calculated all renormalization factors at one-loop level.

Demonstrated BRST invariance and multiplicative renormalizability of the composite operator.

Argued for the existence of gluon-ghost condensates using local composite operator formalism.

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.