Abstract
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n + ν) × (2n + 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.
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Akemann, G., Nagao, T. Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition. J. High Energ. Phys. 2011, 60 (2011). https://doi.org/10.1007/JHEP10(2011)060
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DOI: https://doi.org/10.1007/JHEP10(2011)060