Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential

Abstract

We prove that QCD in the epsilon-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential mu. To this aim we prove a theorem that relates integrals over fermionic and bosonic variables to super-Hermitian or super-Unitary groups also called superbosonization. Our findings extend previous results for the equivalence of the partition functions, spectral densities and the quenched two-point densities. We can show that all k-point density correlation functions agree in both theories for an arbitrary number of quark flavors, for either mu=0 or mu=/=0 taking real or imaginary values. This implies the equivalence for all individual k-th eigenvalue distributions which are particularly useful to determine low energy constants from Lattice QCD with chiral fermions.

arXiv commentv2: typos corrected and comments on echPT at real mu added v3: typos corrected and references added

References in corpus (45)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Riemannian symmetric superspaces and their origin in random matrix theory
• 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
• Non-Hermitean Random Matrix Theory: method of hermitization
• 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
• Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
• Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Distribution of the k-th smallest Dirac operator eigenvalue
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Nonhermitean Random Matrix Models
• Universal Spectral Correlators and Massive Dirac Operators
• Universality of Random-Matrix Results for non-Gaussian Ensembles
• Replica Limit of the Toda Lattice Equation
• The microscopic spectrum of the QCD Dirac operator with finite quark masses
• Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
• Matrix Models and QCD with Chemical Potential
• Universality for eigenvalue correlations at the origin of the spectrum
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• A New Method for Determining $F_{\pi }$ on the Lattice
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• On the supersymmetric partition function in QCD-inspired random matrix models
• Distributions of Dirac Operator Eigenvalues
• Effective Low Energy Theories and QCD Dirac Spectra
• Generalizations of some integrals over the unitary group
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Random matrix models with log-singular level confinement: method of fictitious fermions
• Ratios of characteristic polynomials in complex matrix models
• Bosonization for disordered and chaotic systems
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Extracting $F_{\pi }$ from small lattices: unquenched results
• The Replica Limit of Unitary Matrix Integrals
• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• On matrix model partition functions for QCD with chemical potential
• The Supersymmetric Method in Random Matrix Theory and Applications to QCD
• Effective Lagrangian for strongly coupled domain wall fermions

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• Complex Langevin Dynamics for chiral Random Matrix Theory
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• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Chiral Lagrangian and spectral sum rules for dense two-color QCD
• Chiral random matrix theory for two-color QCD at high density
• The Chiral Condensate in a Finite Volume
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Random matrix analysis of the QCD sign problem for general topology
• Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
• Finite size scaling of meson propagators with isospin chemical potential
• Subsets and the canonical partition functions
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Staggered chiral random matrix theory
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• A subset solution to the sign problem in random matrix simulations
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• The QCD sign problem and dynamical simulations of random matrices
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature
• Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential
• Exploring the Aoki regime
• Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential