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.
Highlights
The dual superconductivity picture [1,2,3,4] represents one of the most popular attempts to explain color confinement
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
In this paper we investigated the decomposition of the G 1⁄4 SUðNÞ Yang-Mills theory with respect to the stability group H 1⁄4 UðN − 1Þ
Summary
The dual superconductivity picture [1,2,3,4] represents one of the most popular attempts to explain color confinement. The resulting reformulation of the Yang-Mills theory has been first performed in the SUð2Þ case [22] and later extended to the general SUðNÞ case [23] It turned out, that for N ≥ 3 the decomposition is no longer unique, as the gauge field is decomposed into the part lying in the stability group H and its remainder SUðNÞ/H. Even though this procedure is reminiscent of a “gauge fixing” from the extended Yang-Mills theory to a theory equipollent to the original SUðNÞ Yang-Mills theory, it should be remarked that the idea behind it is conceptually different from the usual gauge fixing Another key aspect within this reformulation is that one could introduce a gauge invariant mass term for the homogeneously transforming coset field [22], m2XTrG/HðX μX μÞ: ð1:3Þ. The one-loop effective potential for the composite operator is calculated and the existence of the condensate is discussed
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