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.

v2: typos corrected and comments on echPT at real mu added v3: typos corrected and references added

References in corpus (6)

• Matrix Models and QCD with Chemical Potential
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• Bosonization for disordered and chaotic systems
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
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Cited by in corpus (17)

• 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
• The Chiral Condensate in a Finite Volume
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Random matrix analysis of the QCD sign problem for general topology
• Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
• Subsets and the canonical partition functions
• Finite size scaling of meson propagators with isospin 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 for the Wilson Dirac Operator
• The QCD sign problem and dynamical simulations of random matrices
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor