Chiral Random Matrix Theory and Chiral Perturbation Theory

Abstract

Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.

Lectures given as mini-course at the XIV Mexican School on Particles and Fields 2010

References in corpus (17)

• Microscopic Spectrum of the Wilson Dirac Operator
• Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• The Chiral Condensate in a Finite Volume
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• The epsilon regime with Wilson fermions
• Observations on the Wilson fermions in the epsilon regime
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Finite size scaling of meson propagators with isospin chemical potential
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Partially quenched chiral perturbation theory in the epsilon-regime
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• The epsilon regime with twisted mass Wilson fermions

Cited by in corpus (7)

• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Hydrodynamics of the Chiral Dirac Spectrum
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature