Supersymmetric k field theories and defect structures

We construct supersymmetric k field theories (i.e., theories with a nonstandard kinetic term) in 1 + 1 and 2 + 1 dimensions such that the bosonic sector just consists of a nonstandard kinetic term plus a potential. Further, we study the possibility of topological defect formation in these supersymmetric models. Finally, we consider more general supersymmetric k field theories where, again, topological defects exist in some cases.