Non-Abelian walls in supersymmetric gauge theories

Abstract

The Bogomol'nyi-Prasad-Sommerfield (BPS) multiwall solutions are constructed in supersymmetric $\mathrm{U}({N}_{\mathrm{C}})$ gauge theories in five dimensions with ${N}_{\mathrm{F}}(>{N}_{\mathrm{C}})$ hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge coupling. The generic wall solutions require nontrivial configurations for either gauge fields or off diagonal components of adjoint scalars depending on the gauge. Effective theories of moduli fields are constructed as world volume gauge theories. 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 $\mathrm{S}\mathrm{U}({N}_{\mathrm{F}})/[\mathrm{S}\mathrm{U}({N}_{\mathrm{C}})\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{U}({N}_{\mathrm{F}}\ensuremath{-}{N}_{\mathrm{C}})\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]$ endowed with a deformed metric.