Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories

@article{Kneipp2008HitchinsEA,
title={Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories},
author={Marco A.C. Kneipp},
journal={Journal of High Energy Physics},
year={2008},
volume={2008},
pages={049-049}
}
• M. Kneipp
• Published 4 January 2008
• Mathematics
• Journal of High Energy Physics
We show that ZN string's BPS equations are equivalent to the Hitchin's equations (or self-duality equation) and also to the zero curvature condition. We construct the general form for BPS ZN string solutions for arbitrary simple gauge groups with non-trivial center. Depending on the vacuum solutions considered, the ZN 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.
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