Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions

Abstract

Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of the three classical matrix ensembles: unitary, orthogonal and symplectic, all of which describe universality classes of $SU(N_c)$ gauge theories with $N_f$ fermions in different representations. Random matrix theory universality is reconsidered in this new light.

arXiv commentLaTeX, 18 pages, few more misprints corrected, Version to appear in Nucl. Phys. B

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• Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions
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• Finite volume partition functions and Itzykson-Zuber integrals
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Cited by in corpus (39)

• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Quark spectra, topology and random matrix theory
• Distribution of the k-th smallest Dirac operator eigenvalue
• Characteristic Polynomials of Complex Random Matrix Models
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Determination of the chiral condensate from QCD Dirac spectrum on the lattice
• Determination of the chiral condensate from 2+1-flavor lattice QCD
• Eigenvalue spectrum of massless Dirac operators on the lattice
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Microscopic universality with dynamical fermions
• Spectral Properties of the Overlap Dirac Operator in QCD
• The Chiral Condensate in a Finite Volume
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• QCD3 and the Replica Method
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
• Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
• The orthogonal ensemble of random matrices and QCD in three dimensions
• Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions
• Spectral Universality of Real Chiral Random Matrix Ensembles
• Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
• Three-dimensional QCD in the adjoint representation and random matrix theory
• Massive chiral random matrix ensembles at beta = 1 & 4 : QCD Dirac operator spectra
• Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory
• Odd-flavored QCD_3 and Random Matrix Theory
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Interpolation between the epsilon and p regimes
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Random matrix model for QCD_3 staggered fermions
• The Replica Method and Toda Lattice Equations for QCD_3
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Comparing lattice Dirac operators with Random Matrix Theory