arXiv 1811.056132018-11-14hep-th

具有$U(N-1)$稳定群的$SU(N)$ Yang-Mills理论中的复合算子和凝聚

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

Matthias Warschinke, Ryutaro Matsudo, Shogo Nishino, Toru Shinohara, Kei-Ichi Kondo

备注：: Talk given at the XIIIth Quark Confinement and the Hadron Spectrum 2018, Maynooth

摘要：

最近，为了从双超导电性的观点理解禁闭，受到Cho-Faddeev-Niemi分解的启发，$SU(N)$ Yang-Mills理论的重新表述已经被发展。红外线阿贝尔优势的概念在实现这一概念中起着重要作用，通过对晶格的数值模拟，发现了证据，例如某些胶子自由度的动力学质量生成。一个有希望的分析尝试来解释这种质量的产生是通过质量维度2的凝聚。在这次演讲中，我们想把重点放在以前被忽视的最小选项与非阿贝尔$U(N-1)$稳定群的$SU(N)$杨-米尔斯理论，与著名的最大阿贝尔规范，其中分解对应于阿贝尔$U(1)^{N-1}$稳定群。我们对这个新的分解进行了一个彻底的单圈分析，根据这个理论的重正化性，在单圈水平上计算了所有的标准重整化群函数。随后，我们定义了一个适当的混合胶子鬼复合算子的质量维2作为候选人的凝聚在这个理论，并证明其（上壳）BRST不变性和乘法重整化。最后，在局部复合算子形式下讨论了凝聚的存在性。

英文摘要：

Recently, a reformulation of the $SU(N)$ Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition has been developed in order to understand confinement from the viewpoint of the dual superconductivity. The concept of infrared Abelian dominance plays an important role in the realization of this concept and through numerical simulations on the lattice, evidence was found for example in the form of the dynamical mass generation for certain gluon degrees of freedom. A promising analytical attempt to explain the generation of such masses is through condensates of mass dimension two. In this talk, we want to focus on the reformulated $SU(N)$ Yang-Mills theory in the previously overlooked minimal option with the non-Abelian $U(N-1)$ stability group, in contrast to the famous maximal Abelian gauge, where the decomposition corresponds to the Abelian $U(1)^{N-1}$ stability group. We proceed with a thorough one-loop analysis of this novel decomposition, calculating all standard renormalization group functions at one-loop level in light of the renormalizability of this theory. We subsequently define an appropriate mixed gluon-ghost composite operator of mass dimension two as the candidate for the condensate within this theory and prove its (on-shell) BRST invariance and the multiplicative renormalizability. Finally, the existence of the condensate is discussed within the local composite operator formalism.

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英文摘要：

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