Individual eigenvalue distributions for chGSE-chGUE crossover and determination of low-energy constants in two-color QCD+QED

Shinsuke Nishigaki, Takuya Yamamoto
2015 Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)   unpublished
We compute statistical distributions of individual low-lying eigenvalues of random matrix ensembles interpolating chiral Gaussian symplectic and unitary ensembles. To this aim we use the Nyström-type discretization of Fredholm Pfaffians and resolvents of the dynamical Bessel kernel containing a single crossover parameter ρ. The ρ-dependent distributions of the four smallest eigenvalues are then used to fit the Dirac spectra of modulated SU(2) lattice gauge theory, in which the reality of the
more » ... ggered SU(2) Dirac operator is weakly violated either by the U(1) gauge field or by a constant background flux. Combined use of individual eigenvalue distributions is effective in reducing statistical errors in ρ; its linear dependence on the imaginary chemical potential µ I enables precise determination of the pseudo-scalar decay constant F of the SU(2) gauge theory from a small lattice. The U(1)-coupling dependence of an equivalent of F 2 µ 2 I in the SU(2)×U(1) theory is also obtained.
doi:10.22323/1.214.0067 fatcat:t443v2foyncm7fiu3venzzqem4