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

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.