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arXiv · 1711.03388

Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2)$\times$U(1) lattice gauge theory

Takuya Yamamoto·Shinsuke M. Nishigaki
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Abstract

We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nystr\"om-type method of evaluating the Fredholm Pfaffian and resolvents of the quaternion kernel. The one-parameter family of these distributions are shown to fit excellently the Dirac spectra of SU(2) lattice gauge theory with a constant U(1) background or dynamically fluctuating U(1) gauge field, which weakly breaks the pseudo-reality of the unperturbed SU(2) Dirac operator. Observed linear dependence of the crossover parameter with the strength of U(1) perturbations leads to precise determination of the pseudo-scalar decay constant, as well as the chiral condensate in the effective chiral Lagrangian of AI class.

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Takuya Yamamoto, Shinsuke M. Nishigaki. 2017-11-09. Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2)$\times$U(1) lattice gauge theory. https://doi.org/10.1093/ptep/ptx188

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