Superbosonization formula and its application to random matrix theory

Abstract

Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random matrices. We clarify the domain of integration for the supermatrices, and give a demonstration of how the model works by calculating the density of states for an ensemble of almost diagonal matrices. It is also shown how one can reduce the supermatrix model to the conventional sigma model.

18 pages

References in corpus (2)

• Bosonization for disordered and chaotic systems
• Are Bosonic Replicas Faulty?

Cited by in corpus (7)

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• Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
• Integration of Grassmann variables over invariant functions on flat superspaces
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• Handbook Article on Applications of Random Matrix Theory to QCD
• Hyperbolic Hubbard-Stratonovich transformation made rigorous
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor