Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
Aug, 2011Citations per year
Abstract: (arXiv)
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) 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 refs. [20,21]. 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 nu=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.Note:
- 27 pages, 4 figures/ v2 typos corrected, published version
- Matrix Models
- Lattice QCD
- Chiral Lagrangians
- matrix model: random
- perturbation theory: chiral
- operator: Wilson
- operator: Dirac
- partition function
- density: correlation function
- expansion 1/N
References(48)
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