Walls and vortices in supersymmetric non-abelian gauge theories

By Norisuke Sakai, Tokyo Instute of Technology

We consider multi-wall solutions and vortices in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions for the BPS equations are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge coupling. Effective theories of moduli fields are constructed for multi-walls. Nambu-Goldstone and quasi-Nambu-Goldstone scalars are distinguished and worked out. Total moduli space of the BPS non-Abelian walls including all topological sectors is found to be the complex Grassmann manifold SU(N_F) / [SU(N_C)×SU(N_F-N_C) ×U(1)] endowed with a deformed metric. Moduli space of vortices connecting between walls are found to be holomorphic maps from complex plane to the complex Grassmann manifold.