Level spacings of parametric chiral random matrices and two-color QCD with twisted boundary condition

TL;DR

This paper investigates the spectral properties of chiral random matrices transitioning between symmetry classes and relates these findings to lattice gauge theory, enabling the extraction of physical constants like the pion decay constant.

Contribution

It provides a detailed analysis of level spacing and eigenvalue distributions in crossover regimes, linking random matrix theory to lattice QCD with twisted boundary conditions.

Findings

Level spacing distributions fit well with theoretical models.

The crossover parameter rho depends linearly on the imaginary chemical potential mu.

The proportionality constant between rho and mu yields the pion decay constant F.

Abstract

We evaluate level spacing and smallest eigenvalue distributions of chiral random matrix ensembles transiting from symplectic or orthogonal to unitary symmetry classes with a crossover parameter rho. As expected from the effective sigma model description, these results can be fitted perfectly to the fundamental or adjoint staggered Dirac spectrum of SU(2) quenched lattice gauge theory under the imaginary chemical potential (twisting) mu. The linear dependence of the parameter rho on mu determines the pion decay constant F as its proportionality constant.