Nonhermitian supersymmetric partition functions: The case of one bosonic flavor

We discuss the supersymmetric formulation of the nonhermitian β = 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 σ-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 σ-model.