Complex Burgers' equation in 2D SU(N) YM

2008/09/30 by Herbert Neuberger, H. Neuberger · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #Theoretical and Computational Physics #hep-lat #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.physletb.2008.11.009

published as Phys.Lett.B670:235-240,2008 · 10 pages; fixed typo in eq. 37, updated 1 reference and added 2 minor clarifying comments

arxiv created 2008/10/23 · openalex publication_date 2008/11/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two-dimensional pure Yang–Mills theory with gauge group SU(N) is derived from two associated complex Burgers' equations, with viscosity given by 12N. The Wilson loop does not intersect itself and Euclidean space–time is assumed flat and infinite. This result provides an extension of the infinite N solution of Durhuus and Olesen to finite N, but this extension is not unique.

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