Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

TL;DR

This paper develops a supersymmetric nonlinear sigma-model for nonhermitian random matrix partition functions with one bosonic flavor, demonstrating universality across models with similar symmetries and a mass gap.

Contribution

It introduces a symmetry-based derivation of the supersymmetric sigma-model for nonhermitian matrices with one bosonic flavor, applicable to a broad class of models.

Findings

Derived the sigma-model using symmetry arguments.

Confirmed results with superbosonization and polynomial methods.

Showed universality of the sigma-model for models with the same symmetries.

Abstract

We discuss the supersymmetric formulation of the nonhermitian $\beta = 2$ random matrix partition function with one bosonic flavor. This partition function is regularized by adding one conjugate boson and fermion each. A supersymmetric nonlinear $\sigma$-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 $\sigma$-model.