Individual eigenvalue distributions for the Wilson Dirac operator

被引:0
作者
G. Akemann
A. C. Ipsen
机构
[1] Department of Physics,Niels Bohr International Academy and Discovery Center
[2] Bielefeld University,undefined
[3] Niels Bohr Institute,undefined
来源
Journal of High Energy Physics | / 2012卷
关键词
Matrix Models; Lattice QCD; Chiral Lagrangians;
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摘要
We derive the distributions of individual eigenvalues for the Hermitian Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac Operator DW. The framework we provide is valid in the epsilon regime of chiral perturbation theory for any number of flavours Nf and for non-zero low energy constants W6,7,8. It is given as a perturbative expansion in terms of the k-point spectral density correlation functions and integrals thereof, which in some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at fixed chirality ν this expansion truncates after at most ν terms for small lattice spacing a. Explicit examples for the distribution of the first and second eigenvalue are given in the microscopic domain as a truncated expansion of the Fredholm Pfaffian for quenched D5, where all k-point densities are explicitly known from random matrix theory. For the real eigenvalues of quenched DW at small a we illustrate our method by the finite expansion of the corresponding Fredholm determinant of size ν.
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[11]  
Toublan D(2005) = 2 QCD with mixed actions Phys. Rev. D 72 091501-undefined
[12]  
Verbaarschot J(2006)A New method for determining F Phys. Rev. D 73 074023-undefined
[13]  
Basile F(2006) on the lattice Phys. Rev. D 73 105016-undefined
[14]  
Akemann G(2009)Extracting JHEP 11 005-undefined
[15]  
Nishigaki SM(2010) from small lattices: Unquenched results JHEP 06 028-undefined
[16]  
Damgaard PH(2011)Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential JHEP 05 115-undefined
[17]  
Wettig T(2007)Partially quenched chiral perturbation theory in the ǫ-regime at next-to-leading order Nucl. Phys. B 766 34-undefined
[18]  
Damgaard PH(1993)The ǫ-expansion at next-to-next-to-leading order with small imaginary chemical potential Phys. Rev. Lett. 70 3852-undefined
[19]  
Nishigaki SM(1997)Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F Nucl. Phys. B 487 721-undefined
[20]  
Damgaard P(1998)A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential Nucl. Phys. B 518 495-undefined