Effective theory on non-Abelian vortices in six dimensions

Abstract

Non-Abelian vortices in six spacetime dimensions are obtained for a supersymmetric U ( N ) gauge theory with N hypermultiplets in the fundamental representation. Massless (moduli) fields are identified and classified into Nambu–Goldstone and quasi-Nambu–Goldstone fields. Effective gauge theories for the moduli fields are constructed on the four-dimensional world volume of vortices. A systematic method to obtain the most general form of the effective Lagrangian consistent with symmetry is proposed. The moduli space for the multi-vortices is found to be a vector bundle over the complex Grassmann manifold.