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We prove that Wilson loop expectation values for arbitrary simple closedcontours obey an area law up to second order in perturbative two-dimensionalYang-Mills theory. Our analysis occurs within a general family of axial-likegauges, which include and interpolate between holomorphic gauge and theWu-Mandelstam-Liebrandt light cone gauge. Our methods make use of the homotopyinvariance properties of iterated integrals of closed one-forms, which allowsus to evaluate the nontrivial integrals occurring at second order. We closewith a discussion on complex gauge-fixing and deformation of integration cyclesfor holomorphic path integrals to shed light on some of the quantumfield-theoretic underpinnings of our results.

Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge