Semi-Bogomol'nyi-Prasad-Sommerfield sphaleron and its dynamics.

We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore, such a sphaleron-impurity system is very much like usual BPS multisolitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.