Walls in a supersymmetric massive nonlinear sigma model on a complex quadric surface

Abstract

The Bogomol'nyi-Prasad-Sommerfield (BPS) multiwall solutions are constructed in a massive K\"ahler nonlinear sigma model on the complex quadric surface, ${Q}^{N}=\frac{SO(N+2)}{SO(N)\ifmmode\times\else\texttimes\fi{}SO(2)}$ in 3-dimensional space-time. The theory has a nontrivial scalar potential generated by the Scherk-Schwarz dimensional reduction from the massless nonlinear sigma model on ${Q}^{N}$ in 4-dimensional space-time and it gives rise to $2[N/2+1]$ discrete vacua. The BPS wall solutions connecting these vacua are obtained based on the moduli matrix approach. It is also shown that the moduli space of the BPS wall solutions is the complex quadric surface ${Q}^{N}$.