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 Yang-Mills theory in the minimal option with 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.
Keywords
Cite
@article{arxiv.1711.03276,
title = {Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group},
author = {Matthias Warschinke and Ryutaro Matsudo and Shogo Nishino and Toru Shinohara and Kei-Ichi Kondo},
journal= {arXiv preprint arXiv:1711.03276},
year = {2018}
}
Comments
In the latest version, we corrected a previously wrong result for the anomalous dimension of the residual ghosts