Distributions of Dirac Operator Eigenvalues

Abstract

The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated. As a special case, we give examples of the lowest-lying eigenvalue distributions for QCD-like gauge theories without making use of earlier results based on the relation to Random Matrix Theory.

9 pages, 4 figures; typos in appendix corrected, published version

References in corpus (3)

• Replica Limit of the Toda Lattice Equation
• On the supersymmetric partition function in QCD-inspired random matrix models
• Spectral Properties of the Overlap Dirac Operator in QCD

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• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
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• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study on the lattice
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• A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• On the Largest Singular Values of Random Matrices with Independent Cauchy Entries
• Chiral Random Matrix Theory and Chiral Perturbation Theory
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• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
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