Lattice Chiral Gauge Theories Research Articles

Lorentz non-covariance of lattice chiral gauge theories

We show that, in the continuum limit, the four-dimensional chiral gauge theory built from Wilson fermions with radially frozen Higgs fields leads to Lorentz non-covariant terms in the vacuum polarization tensor, despite the gauge invariance of the regularization. The computation is done when n f, the number of flavors, is large.

The decoupling of right-handed neutrinos in chiral lattice gauge theories

The decoupling of the right-handed fermion in the continuum limit is proved for a class of chiral lattice gauge theories for which the right-handed fermion transforms trivially under the gauge group. No tuning is necessary. The theorem follows from a new fermion shift symmetry.

Stochastic quantization of matrix and lattice gauge models

We introduce a stochastic diffusion equation and the Fokker-Planck equation for various matrix models including the $\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(N)$ chiral model and lattice gauge theories. It is shown how to calculate various $\mathrm{U}(N)$ integrals using the stochastic equation. In particular, in the external-field problem, the exact large-$N$ result (in the weak-coupling region) is reproduced and a $\frac{1}{{N}^{2}}$ correction is computed. Also, the order parameter $〈\mathrm{det}U〉$ is calculated up to order $\frac{1}{{\ensuremath{\beta}}^{2}}$. In the $\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(N)$ chiral model, the large-$N$ reduction and quenching is done in the context of stochastic quantization, and the semiclassical results of Bars, Gunaydin, and Yankielowicz for the free energy and the two-point correlation function are derived. In lattice gauge theory, a very simple way of deriving the complete Schwinger-Dyson equations from the Fokker-Planck equation is demonstrated and, as in the chiral model, a reduced, quenched stochastic equation is derived.