Level Spacings of Parametric Chiral Random Matrices and Two-Color QCD with Twisted Boundary Condition

Abstract

We evaluate the level spacing and smallest eigenvalue distributions of chiral random matrix ensembles transiting from symplectic or orthogonal to unitary symmetry classes with a crossover parameter ρ. As expected from the effective σ 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) μ .T he linear dependence of the parameter ρ on μ determines the pion decay constant F as its proportionality constant.