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

High Energy Physics - Theory 2008-12-18 v3 High Energy Physics - Lattice Mathematical Physics math.MP

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 1/(2N). 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.

Keywords

Cite

@article{arxiv.0809.1238,
  title  = {Complex Burgers' equation in 2D SU(N) YM},
  author = {H. Neuberger},
  journal= {arXiv preprint arXiv:0809.1238},
  year   = {2008}
}

Comments

10 pages; fixed typo in eq. 37, updated 1 reference and added 2 minor clarifying comments

R2 v1 2026-06-21T11:17:43.826Z