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

TL;DR

This paper introduces a new chiral two-matrix random matrix theory to analytically compute spectral correlation functions of Dirac operator eigenvalues with imaginary chemical potential, applicable to lattice gauge theory.

Contribution

It provides explicit formulas for spectral correlation functions of a novel chiral two-matrix model, extending results to finite size and microscopic limits, and connects to physical observables.

Findings

Derived explicit spectral correlation functions for the new model.

Extended results to non-chiral ensembles and finite sizes.

Confirmed agreement with previous effective field theory computations.

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.