Symmetry Crossover Protecting Chirality in Dirac Spectra

Abstract

We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.

arXiv comment42 pages, 3 figures, PACS numbers: 02.10.Yn,05.50.+q,11.15.Ex,11.15.Ha,12.38.-t

References in corpus (60)

• QCD at finite isospin density
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Generic Rules for High Temperature Dimensional Reduction and Their Application to the Standard Model
• On the Foundations of Chiral Perturbation Theory
• Free Energy of QCD at High Temperature
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random matrix model of QCD at finite density and the nature of the quenched limit
• Measurement of $J/\psi$ helicity distributions in inelastic photoproduction at HERA
• QCD-like Theories at Finite Baryon Density
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• QCD-like Theories at Finite Baryon and Isospin Density
• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• QCD phase diagram for nonzero isospin-asymmetry
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
• Two-colour QCD at non-zero quark-number density
• Dual quark condensate and dressed Polyakov loops
• Random matrix theory and $QC{D}_3$
• Microscopic Spectrum of the Wilson Dirac Operator
• An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator
• Superbosonization of invariant random matrix ensembles
• Singular values of the Dirac operator in dense QCD-like theories
• Matrix Models and QCD with Chemical Potential
• New findings for topological excitations in SU(3) lattice gauge theory
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• Chiral Lagrangian and spectral sum rules for dense two-color QCD
• Anomalous Chiral Symmetry Breaking above the QCD Phase Transition
• Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition
• Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
• Universal Massive Spectral Correlators and QCD_3
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions
• The dyonic picture of topological objects in the deconfined phase
• QCD with one compact spatial dimension
• A Quark-Antiquark Condensate in Three-Dimensional QCD
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• The supersymmetry method of random matrix theory
• Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
• Quantum phase transitions and new scales in QCD-like theories
• Dirac Spectra of 2-dimensional QCD-like theories
• Staggered chiral random matrix theory
• Two-color QCD in 3D at finite baryon density
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Shift of Symmetries of Naive Fermions in QCD-like Lattice Theories
• Determining F_pi from spectral sum rules
• Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD
• Supersymmetry in Random Matrix Theory
• Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model
• Random matrix model for QCD_3 staggered fermions
• Phases of circle-compactified QCD with adjoint fermions at finite density
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Instanton-dyon ensembles reproduce deconfinement and chiral restoration phase transitions
• Global Symmetries of Naive and Staggered Fermions in Arbitrary Dimensions
• Chiral random matrix theory for staggered fermions

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• Chiral random matrix theory for colorful quark-antiquark condensates