Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “Ø-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the Ø-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.