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.

arXiv comment31 pages 2 figures, v2 missing term in partially quenched results inserted, fig 2 updated

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• Random matrices beyond the Cartan classification
• 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
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• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• The Interpolating Airy Kernels for the beta=1 and beta=4 Elliptic Ginibre Ensembles
• Finite size scaling of meson propagators with isospin chemical potential
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Staggered chiral random matrix theory
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• A note on the limiting mean distribution of singular values for products of two Wishart random matrices
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Chiral Random Matrix Theory and Chiral Perturbation Theory
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• Large n limit for the product of two coupled random matrices
• The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant
• Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential
• Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices