Massive random matrix ensembles at beta = 1 & 4 : QCD in three dimensions

Abstract

The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and symplectic ensembles of random matrices. Using this correspondence, we compute finite-volume QCD partition functions and correlation functions of Dirac operator eigenvalues in a presence of finite quark masses of the order of the smallest Dirac eigenvalue. These novel correlation functions, expressed in terms of quaternion determinants, are reduced to conventional results for the Gaussian ensembles in the quenched limit.

26 pages, REVTeX 3.1 + mathlett.sty (attached), 4 figures

References in corpus (5)

• Spectra of massive and massless QCD Dirac operators: A novel link
• 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
• Massive chiral random matrix ensembles at beta = 1 & 4 : QCD Dirac operator spectra
• Three-dimensional QCD in the adjoint representation and random matrix theory

Cited by in corpus (9)

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• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
• Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
• Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Bott Periodicity and Realizations of Chiral Symmetry in Arbitrary Dimensions
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Comment on Dirac spectral sum rules for QCD_3