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arXiv 2103.17136hep-thhep-lat
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矢量场、RG流和突现规范对称性

Vector fields, RG flows and emergent gauge symmetry

Daniel Nogradi

摘要:

我们考虑具有整体SU(N)对称性和无质量耦合的四维矢量场的最一般的微扰重整化理论。拉格朗日量包含1个二次、2个三次和4个四次耦合。这组7个耦合之间的RG流计算1-循环和丰富的相图绘制出来,特别是它示出了有限数量的渐近自由RG流存在对应于非平凡的不动点的比率的耦合。这些理论都不是规范理论,即只具有整体SU(N)不变性,而不是局部不变性。我们还包括最一般的鬼耦合,仍然与全球SU(N)的不变性,并计算RG流到1-回路的所有9个耦合。再次渐近自由RG流存在非平凡的不动点的比率的耦合。结果表明,杨米尔斯理论出现在一个特定的不动点。在其他不动点的理论是边缘相关的规范对称性违反杨米尔斯理论的微扰。对大N极限也进行了详细的研究。

英文摘要:

We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.

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