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.
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