# 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} }

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.

## 12 Citations

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