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.

• Received 27 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.065032