We construct supersymmetric K field theories (i.e., theories with a
non-standard 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.Comment: Latex, 6 figures, 27 page