D-brane construction for non-Abelian walls

Abstract

Supersymmetric $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}$ massive hypermultiplets in the fundamental representation is given by the brane configuration made of ${N}_{\mathrm{C}}$ fractional $\mathrm{D}p$-branes stuck at the ${\mathbf{Z}}_{2}$ orbifold singularity on ${N}_{\mathrm{F}}$ separated $\mathrm{D}(p+4)$-branes. We show that non-Abelian walls in this theory are realized as kinky fractional $\mathrm{D}p$-branes interpolating between $\mathrm{D}(p+4)$-branes. Wall solutions and their duality between ${N}_{\mathrm{C}}$ and ${N}_{\mathrm{F}}\ensuremath{-}{N}_{\mathrm{C}}$ imply extensions of the s-rule and the Hanany-Witten effect in brane dynamics. We also find that the reconnection of fractional D-branes occurs in this system. Diverse phenomena in non-Abelian walls found in field theory can be understood very easily by this brane configuration.