Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case

Abstract

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary-symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formula. We express our results in a unifying way. We also give explicit expressions for all one-point functions and discuss features of the higher order correlations.

37 pages

References in corpus (5)

• Superbosonization of invariant random matrix ensembles
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Bosonization for disordered and chaotic systems
• The supersymmetry method of random matrix theory
• Integration of Grassmann variables over invariant functions on flat superspaces

Cited by in corpus (1)

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