Baryons as Vortexes on the $\eta^{\prime}$ Domain Wall

Abstract

We show that the recent construction of $N_f=1$ baryons on the $\eta^\prime$ domain wall can be understood as vortexes of the principal effective theory -- the Chern-Simons-Higgs theory -- on a 2+1-dimensional sheet. This theory has a series of vertex solutions, and the vortex with unit topological charge naturally spins $N_c/2$, which coincides with the spin of the one-flavor baryon in QCD. Since the $N_c$ scaling of the vortexes is the same as that of baryons, baryons can be regarded as vortexes. By virtue of the particle-vortex symmetry, the dual Zhang-Hansson-Kivelson theory indicates that the quark carries topological charge $1/N_c$ and obeys fractional statistics. The generalization to arbitrary $N_f$ is also discussed.