A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential

Abstract

We solve a new chiral Random Two-Matrix Theory by means of biorthogonal polynomials for any matrix size $N$. By deriving the relevant kernels we find explicit formulas for all $(n,k)$-point spectral (mixed or unmixed) correlation functions. In the microscopic limit we find the corresponding scaling functions, and thus derive all spectral correlators in this limit as well. We extend these results to the ordinary (non-chiral) ensembles, and also there provide explicit solutions for any finite size $N$, and in the microscopic scaling limit. Our results give the general analytical expressions for the microscopic correlation functions of the Dirac operator eigenvalues in theories with imaginary baryon and isospin chemical potential, and can be used to extract the tree-level pion decay constant from lattice gauge theory configurations. We find exact agreement with previous computations based on the low-energy effective field theory in the two special cases where comparisons are possible.

31 pages 2 figures, v2 missing term in partially quenched results inserted, fig 2 updated

References in corpus (7)

• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Extracting $F_{\pi }$ from small lattices: unquenched results
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Determining F_pi from spectral sum rules

Cited by in corpus (10)

• Random matrices beyond the Cartan classification
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• 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
• Finite size scaling of meson propagators with isospin chemical potential
• Staggered chiral random matrix theory
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
• Individual Eigenvalue Distributions for the Wilson Dirac Operator