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

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

2008-01-04

arxiv.org/abs/0801.0720v2

JHEP 0811:049,2008

Physics

High Energy Physics

High Energy Physics - Theory

13 pages. Some comments and references added; change of a convention (Eq. (9)); version to appear in JHEP

Scientific paper

10.1088/1126-6708/2008/11/049

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.

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