Lattice Chiral Gauge Theory with Finely-Grained Fermions

Abstract

We discuss the problem of formulating the continuum limit of chiral gauge theories ($χ$GT) in the absence of an explicitly gauge-invariant regulator for the fermions. A solution is proposed which is independent of the details of the regulator, wherein one considers two cutoff scales, $Λ_f >> Λ_b$, for the fermions and the gauge bosons respectively. Our recent non-perturbative lattice construction in which the fermions live on a finer lattice than do the gauge bosons, is seen to be an example of such a scheme, providing a finite algorithm for simulating $χ$GT. The essential difference with previous (one-cutoff) lattice schemes is clarified: in our formulation the breakage of gauge invariance is small, $O(Λ^2_b/Λ^2_f)$, and vanishes in the continuum limit. Finally, we argue against 2-D models being significant testing grounds for 4-D regulators of $χ$GT.

10 pages, LateX, no figures. An important reference to Frolov and Slavnov has been added and a confusing typo corrected