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Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition
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Journal Article
Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition
2011
Overview
We introduce a random two-matrix model interpolating between a chiral Hermitian (2
n
+
ν
) × (2
n
+
ν
) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-
n
limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in [
32
,
33
]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with
ν
= 0
,
1 we derive all spectral correlations functions in our model for finite-
n
, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.
Publisher
Springer-Verlag,Springer Nature B.V
Subject
