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非微扰 Lee-Wick 规范理论：走向强耦合下的禁闭与重整化群方程

Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings

Marco Frasca, Anish Ghoshal, Alexey S. Koshelev

备注：
28 pages, 1 figure. Version accepted for publication in Classical and Quantum Gravity. arXiv admin note: text overlap with arXiv:2106.07629
发表信息：
Class. Quantum Grav. 41, 015014 (2024)
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AI总结：

本文研究非阿贝尔 Lee-Wick 规范理论，利用 Kugo-Ojima 方法和 Jacobi 椭圆函数精确解，在强耦合非微扰区域给出禁闭条件与 β 函数，并证明鬼场在红外极限下不再传播。

摘要：

我们考虑一种非阿贝尔 Lee-Wick 规范理论，并讨论 Becchi-Rouet-Stora-Tyutin（BRST）不变性。该理论包含作为动能项扩展的四阶导数，从而在量子化后导致理论中出现大质量鬼场。我们特别利用 Kugo-Ojima 方法，为强耦合区域中的禁闭条件提供了关键线索，并在非微扰区域中得到了 β 函数。这一结果是通过利用相应局域理论的一组以 Jacobi 椭圆函数表示的精确解来实现的。我们得到了与普通 Yang-Mills 理论类似的 β 函数，但主要区别在于，现在截断参数自然地来自 Lee-Wick 重质量标度（M）。我们表明，鬼场在这些区域中的命运是确定的：它们在红外（IR）极限下不再是传播自由度。正如普通情形中所发生的那样，禁闭源于理论的非阿贝尔性质。在极限 M→∞ 下，可以恢复局域非阿贝尔 Yang-Mills 理论的标准结果。

英文摘要：

We consider a non-Abelian Lee--Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin (BRST) invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo-Ojima approach, and obtain the $β-$functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar $β-$function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee-Wick heavy mass scales (M). We show that the fate of the ghosts is fixed in these regimes: they are no more the propagating degrees of freedom in the infrared (IR)-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit $M\rightarrow\infty $, one recovers the standard results for the local non-Abelian Yang-Mills theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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