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arXiv 1005.4173hep-phhep-th
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迹反常、无质量标量和QCD的引力耦合

Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD

Roberta Armillis, Claudio Coriano, Luigi Delle Rose

备注：
25 pages, 9 figures. Revised final version, to be published on Phys. Rev. D
发表信息：
Phys.Rev.D82:064023,2010
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摘要：

描述引力与非阿贝尔规范理论耦合的反常有效作用量可以由反常方程的变分解来确定，正如里格特很久以前所指出的那样。它是由一个非局部的表达，与非局部的相互作用所确定的格林函数的共形协变算子的四阶。在最近的工作中，它已被证明，这种相互作用是介导的一个简单的极点在闵可夫斯基背景下，在红外耦合在无质量的费米子极限的扩展。这一结果依赖于两个辅助领域，一个物理标量和一个鬼，它采取的作用，无质量的复合自由度的原始行动的本地制定。在引力的情况下，两个标量为最近提出的完全基于QCD相变时真空能量行为的红外方法解决暗能量问题提供了基础。作为对这一一般结果的检验，我们对描述非阿贝尔规范理论与引力耦合的有效作用量进行了完整的单圈计算。我们确认的外观异常极有助于跟踪部分的$TJJ$相关器和额外的极点在其无迹部分，在夸克和胶子部门，描述的耦合的能量动量张量（$T$）到两个非阿贝尔规范流（$J$）。

英文摘要：

The anomalous effective action describing the coupling of gravity to a non-abelian gauge theory can be determined by a variational solution of the anomaly equation, as shown by Riegert long ago. It is given by a nonlocal expression, with the nonlocal interaction determined by the Green's function of a conformally covariant operator of fourth order. In recent works it has been shown that this interaction is mediated by a simple pole in an expansion around a Minkowski background, coupled in the infrared in the massless fermion limit. This result relies on the local formulation of the original action in terms of two auxiliary fields, one physical scalar and one ghost, which take the role of massless composite degrees of freedom. In the gravity case, the two scalars have provided ground in favour of some recent proposals of an infrared approach to the solution of the dark energy problem, entirely based on the behaviour of the vacuum energy at the QCD phase transition. As a test of this general result, we perform a complete one-loop computation of the effective action describing the coupling of a non-abelian gauge theory to gravity. We confirm the appearance of an anomaly pole which contributes to the trace part of the $TJJ$ correlator and of extra poles in its trace-free part, in the quark and gluon sectors, describing the coupling of the energy momentum tensor ($T$) to two non abelian gauge currents ($J$).

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