Supersymmetry in the four-dimensional limit

By adopting a dimension-independent definition of the Lagrangian it is found that the action associated with supersymmetric theories in arbitrary dimensions 2<i>l</i> is not an invariant (and the associated spinor current is not conserved) except for <i>l</i>=2. Nevertheless the spinor Ward identities are anomaly free because the offending terms disappear in four dimensions to all orders in <i>ħ</i>.