Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation

Abstract

Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce integrals over functions of supersymmetric Wishart-matrices to integrals over quadratic supermatrices of certain symmetries.

27 pages, 1 figure

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• Superbosonization of invariant random matrix ensembles
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• Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
• Non-extensive Random Matrix Theory - A Bridge Connecting Chaotic and Regular Dynamics