Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories
High Energy Physics - Theory
2009-12-15 v2 High Energy Physics - Lattice
Exactly Solvable and Integrable Systems
Abstract
We show that Z(N) string's BPS equations are equivalent to the Hitchin's equations (or self-duality equation) and also to the zero curvature condition. We construct a general form for BPS Z(N) string solutions for arbitrary simple gauge groups with non-trivial center. Depending on the vacuum solutions considered, the Z(N) string's BPS equations reduce to different two dimensional integrable field equations. For a particular vacuum we obtain the equation of affine Toda field theory.
Keywords
Cite
@article{arxiv.0801.0720,
title = {Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories},
author = {Marco A. C. Kneipp},
journal= {arXiv preprint arXiv:0801.0720},
year = {2009}
}
Comments
13 pages. Some comments and references added; change of a convention (Eq. (9)); version to appear in JHEP