Non-Abelian Vortices of Higher Winding Numbers

Giacomo Marmorini; Keisuke Ohashi; Kenichi Konishi; Minoru Eto; Muneto Nitta; Naoto Yokoi; Walter Vinci

Non-Abelian Vortices of Higher Winding Numbers

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arxiv hep-th/0607070 v2 pith:NWOHKPQZ submitted 2006-07-11 hep-th astro-phhep-phmath.DG

Minoru Eto , Kenichi Konishi , Giacomo Marmorini , Muneto Nitta , Keisuke Ohashi , Walter Vinci , Naoto Yokoi This is my paper

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keywords vorticesmodulispaceaxiallycontainsflavorsgaugehep-th

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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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