Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature

Abstract

In the $\epsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting kernel and correlation functions in this class, which is the class of polynomial ensembles. We prove the equivalence between this new determinantal representation of the microscopic eigenvalue correlation functions and existing results in terms of determinants of different sizes, for an arbitrary number of quark flavours, with and without temperature, and extend them to non-zero topology. These results all agree and are thus universal when measured in units of the temperature dependent chiral condensate, as long as we stay below the chiral phase transition.

arXiv comment26 pages; v2: minor changes (reference added, typos corrected and some clarification), to appear in JHEP

References in corpus (50)

• On the Phase Diagram of QCD
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Random Matrix Theory and Chiral Symmetry in QCD
• Random matrix model of QCD at finite density and the nature of the quenched limit
• Biorthogonal ensembles
• Universality of random matrices in the microscopic limit and the Dirac operator spectrum
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• 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
• Finite volume partition functions and Itzykson-Zuber integrals
• Characteristic Polynomials of Complex Random Matrix Models
• A random matrix model for chiral symmetry breaking
• Microscopic Spectrum of the Wilson Dirac Operator
• Universal Spectral Correlators and Massive Dirac Operators
• Pion Dynamics at Finite Temperature
• Universality of correlation functions of hermitian random matrices in an external field
• An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices
• A note on biorthogonal ensembles
• The microscopic spectrum of the QCD Dirac operator with finite quark masses
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Universal spectral correlations of the Dirac operator at finite temperature
• The chiral phase transition in a random matrix model with molecular correlations
• On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD
• The Chiral Condensate in a Finite Volume
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• Consistency Conditions for Finite-Volume Partition Functions
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Universality of Correlation Functions in Random Matrix Models of QCD
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Critical Scaling at Zero Virtuality in QCD
• Microscopic Universality and the Chiral Phase Transition in two Flavor QCD
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Spectral correlations of the massive QCD Dirac operator at finite temperature
• Finite size scaling of meson propagators with isospin chemical potential
• Dirac Spectra of 2-dimensional QCD-like theories
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• On characteristic polynomials for a generalized chiral random matrix ensemble with a source
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Random Matrix Theory and Quantum Chromodynamics
• The topological structures in strongly coupled QGP with chiral fermions on the lattice
• QCD, Wick's Theorem for KdV $\tau$-functions and the String Equation
• Shift of Symmetries of Naive Fermions in QCD-like Lattice Theories
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
• Averages of products and ratios of characteristic polynomials in polynomial ensembles

Cited by in corpus (1)

• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit