Non-Abelian Vortices of Higher Winding Numbers

Details Non-Abelian Vortices of Higher Winding Numbers Non-Abelian Vortices of Higher Winding Numbers

2006-07-11

arxiv.org/abs/hep-th/0607070v2

Phys.Rev.D74:065021,2006

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 1 figure, the final version published in PRD

Scientific paper

10.1103/PhysRevD.74.065021

We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of co-axial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto-Tong (hep-th/0506022) and Auzzi-Shifman-Yung (hep-th/0511150). We find that it is a weighted projective space WCP^2_(2,1,1)=CP^2/Z_2. This manifold contains an A_1-type (Z_2) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are then generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.

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