Abstract

We construct the nonminimal linear representations of the N = 4 extended supersymmetry in one-dimension. They act on eight bosonic and eight fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N = 5 linear representations is given. Two types of N = 4 sigma-models based on nonminimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained prepotential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3533761]