A comparison of the superbosonization formula and the generalized Hubbard–Stratonovich transformation

Abstract

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 HubbardStratonovich 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.

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

“…It naturally appears in superbosonization [49][50][51] which can be used to directly map random matrix theory to a finite dimensional version of the chiral partition function [52]. For the quenched theory where N f = 0, the partition function drastically simplifies…”

The Correlated Jacobi and the Correlated Cauchy–Lorentz Ensembles

“…(19) we have used the superbosonization formula [40][41][42]. We use this representation in sections 4 and 6.…”

“…Alternative to the superbosonization formula one can also choose the generalized HubbardStratonovich transformation [42,44,45], see third equality of Eq. (19), which we employ in section 5.…”

“…(19), which we employ in section 5. The superbosonization formula and the generalized Hubbard-Stratonovich transformation are equivalent [42]. The first can be understood as the contour representation of the latter which is some kind of a high dimensional residue theorem.…”

“…The dimension of the supermatrix model is (2|2) × (2|2) and thus twice as large as for the kernel of the complex matrices. We apply the generalized Hubbard-Stratonovich transformation [42,44,45] for k = 1, third equality of Eq. (19), which explicitly reads in this case…”