Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

Abstract

We discuss the supersymmetric formulation of the nonhermitian ${\hat{I}}^2=2$ random matrix partition function with one bosonic flavor. This partition function is regularized by adding one conjugate boson and fermion each. A supersymmetric nonlinear $\ddot{I}ƒ$-model for the resulting Goldstone degrees of freedom is obtained using symmetry arguments only. For a Gaussian probability distribution the same results are derived using superbosonization and the complex orthogonal polynomial method. The symmetry arguments apply to any model with the same symmetries and a mass gap, and demonstrate the universality of the nonlinear $\ddot{I}ƒ$-model.

17 pages, 0 figures. Section II extended. Version to appear in Nucl.Phys.B