Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory

Abstract

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensemble. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N_c), N_c=2, 3.

3 pages, revtex, 2 postscript figures

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Cited by in corpus (15)

• Random Matrix Theory and Chiral Symmetry in QCD
• Effective Low Energy Theories and QCD Dirac Spectra
• Spectra of massive and massless QCD Dirac operators: A novel link
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Eigenvalue Distributions of the QCD Dirac Operator
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Staggered Fermions and Gauge Field Topology
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Spectral Universality of Real Chiral Random Matrix Ensembles
• Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
• New universality classes of the non-Hermitian Dirac operator in QCD-like theories
• Polyakov loops and spectral properties of the staggered Dirac operator
• Determining F_pi from spectral sum rules
• Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background
• Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory