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arXiv 1912.03087hep-thgr-qc
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QCD中Lorentz对称性破坏与渐近自由的挫折

Lorentz Symmetry Violation in QCD and the Frustration of Asymptotic Freedom

I. T. Drummond

备注：
20 pages, 8 figures, further references, minor text changes
发表信息：
Phys. Rev. D 101, 085004 (2020)
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摘要：

本文研究了洛伦兹对称性破缺（LSV）对夸克在基本表象中的SU（N）规范理论的高能行为的影响。该方法是类似的QED处理在以前的文件。与QED相反，标准洛伦兹不变QCD是渐近自由的。我们的目标是探索在高能量的重整化群的结构，因此弱耦合，而不需要洛伦兹对称性破缺是小的。最简单类型的LSV使理论在洛伦兹群的一个子群下保持不变，该子群保持（类时）4-向量。我们详细研究了这种情况，发现渐近自由是受挫。也就是说，在足够高的能量下，运行耦合常数在再次增加之前达到最小值，而LSV参数无限制地增加。

英文摘要：

We study the effect of Lorentz symmetry violation (LSV) on the behaviour at high energy of SU(N) gauge theory with quarks in the fundamental representation. The approach is similar to that for QED treated in a previous paper. In contrast to QED, standard Lorentz invariant QCD is asymptotically free. Our aim is to explore the structure of the renormalisation group at high energy and hence weak coupling without requiring the Lorentz symmetry breaking to be small. The simplest type of LSV leaves the theory invariant under a subgroup of the Lorentz group that preserves a (time-like) 4-vector. We examine this case in detail and find that asymptotic freedom is frustrated. That is, at sufficiently high energy the running coupling constant attains a minimum value before increasing again, while the LSV parameter increases without bound.

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