Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2011-12-02
Physics
High Energy Physics
High Energy Physics - Lattice
7 pages, Latex, talk at Lattice 2011, Squaw Valley, July 10-16, 2011
Scientific paper
Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wilson Dirac operator in the $\epsilon$-domain of QCD with dynamical quarks. We have also obtained the distribution of the chiralities over the real eigenvalues of the Wilson Dirac operator for any number of flavors. All results have been derived for a fixed index of the Dirac operator. An important effect of dynamical quarks is that they completely suppress the inverse square root singularity in the spectral density of the Hermitian Wilson Dirac operator. The analytical results are given in terms of an integral over a diffusion kernel for which the square of the lattice spacing plays the role of time. This approach greatly simplifies the expressions which we here reduce to the evaluation of two-dimensional integrals.
Splittorff Kim
Verbaarschot Jacobus J. M.
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