广义轴规范下二维Yang-Mills的威尔逊圈面积律
Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge
摘要：
证明了在微扰二维Yang-Mills理论中，任意简单闭合轮廓的威尔逊圈期望值在二阶以下服从面积律。我们的分析发生在一个一般的家庭的轴向一样的规范，其中包括和全纯规范和吴-曼德尔菲-Liebrandt光锥规范之间的插值。我们的方法利用同伦不变性性质的迭代积分的封闭的一种形式，这使我们能够评估发生在二阶的非平凡积分。最后，我们讨论了复杂的规范固定和变形的全纯路径积分的积分周期，揭示了我们的结果的量子场论基础。
英文摘要：
We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebrandt light cone gauge. Our methods make use of the homotopy invariance properties of iterated integrals of closed one-forms, which allows us to evaluate the nontrivial integrals occurring at second order. We close with a discussion on complex gauge-fixing and deformation of integration cycles for holomorphic path integrals to shed light on some of the quantum field-theoretic underpinnings of our results.
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