Effective Low Energy Theories and QCD Dirac Spectra

Abstract

We analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra at nonzero chemical potential (with eigenvalues scattered in the complex plane) in terms of an effective low energy theory.

Invited talk at the 10th International Conference on Recent Progress in Many-Body Theories (MBX), Seattle, September 1999, 13 pages, Latex, with 1 figure, uses ws-p9-75x6-50.cls

References in corpus (2)

• On two-color QCD with baryon chemical potential
• Topology and the Dirac Operator Spectrum in Finite-Volume Gauge Theories

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• The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• Thermodynamics of chiral symmetry at low densities
• Ladder-QCD at finite isospin chemical potential
• Breakdown of staggered fermions at nonzero chemical potential
• A New Method for Determining $F_{\pi }$ on the Lattice
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Diquark and Pion Condensation in Random Matrix Models for two-color QCD
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• The solution of a chiral random matrix model with complex eigenvalues
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Critical statistics for non-Hermitian matrices
• QCD in One Dimension at Nonzero Chemical Potential
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• The Realization of the Sharpe-Singleton Scenario
• On matrix model partition functions for QCD with chemical potential
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Finite size scaling of meson propagators with isospin chemical potential
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
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• Baryon Number Dirac Spectrum in QCD
• A subset solution to the sign problem in random matrix simulations
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor
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• The Fluctuations of the Quark Number and of the Chiral Condensate
• Chiral Symmetry Breaking at Nonzero Chemical Potential
• Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential