Aug 23 – 28, 2010
Europe/Berlin timezone

Maximally Non-Abelian Vortices from Self-dual Yang--Mills Fields

Aug 23, 2010, 4:46 PM
Hörsaal I (Bonn)

Hörsaal I


Nussallee 12


Prof. Norisuke Sakai (tokyo woman's christian university)


A particular dimensional reduction of SU(2N) Yang-Mills theory on Sigma x S^2, with Sigma a Riemann surface, yields an S(U(N) x U(N)) gauge theory on Sigma, with a matrix Higgs field. The SU(2N) self-dual Yang--Mills equations reduce to Bogomolny equations for vortices on Sigma. These equations are formally integrable if Sigma is the hyperbolic plane, and we present a subclass of solutions.


The generalization of abelian Higgs vortices to the non-abelian case has recently gained much attention. They may play important role in understanding confinement in QCD, for instance. Witten has discovered that axially symmetric (SO(3) invariant) instantons in SU(2) gauge group can be mapped to U(1) vortices on a hyperbolic plane. This dimensional reduction allowed exact solutions for vortices. We have found a new dimensional reduction of SO(3) invariant instantons in SU(2N) gauge group to obtain non-Abelian vortices of SU(N)xSU(N)xU(1) gauge group on the hyperbolic plane. We have obtained a class of exact solutions for U(1)^N subgroup. Orientational moduli of the non-abelian vortices are still to be worked out.

Primary author

Prof. Norisuke Sakai (tokyo woman's christian university)


Prof. nicholas manton (damtp, university of cambridge)

Presentation materials