Winding number and non-BPS bound states of walls in nonlinear sigma models

Non-supersymmetric multi-wall configurations are generically unstable. It is proposed that the stabilization in compact space can be achieved by introducing a winding number into the model. A BPS-like bound is studied for the energy of configuration with nonvanishing winding number. Winding number is implemented in an ${\cal N}=1$ supersymmetric nonlinear sigma model with two chiral scalar fields and a bound states of BPS and anti-BPS walls is found to exist in noncompact spaces. Even in compactified space $S^1$, this nontrivial bound state persists above a critical radius of the compact dimension.