Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

Details Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

2008-02-19

arxiv.org/abs/0802.2660v2

Nucl.Phys.B803:381-404,2008

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.nuclphysb.2008.06.003

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.

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