Lattice regularization of chiral gauge theories to all orders of perturbation theory

TL;DR

This paper demonstrates that chiral gauge theories can be consistently formulated on a lattice to all orders in perturbation theory, maintaining gauge symmetry and anomaly cancellation using Ginsparg-Wilson relations.

Contribution

It provides a rigorous proof that lattice regularization preserves gauge invariance and anomaly cancellation for chiral gauge theories at all perturbative orders.

Findings

Gauge invariance is maintained on the lattice.

Anomaly cancellation is proven at all orders.

Construction is valid for any compact gauge group.

Abstract

In the framework of perturbation theory, it is possible to put chiral gauge theories on the lattice without violating the gauge symmetry or other fundamental principles, provided the fermion representation of the gauge group is anomaly-free. The basic elements of this construction (which starts from the Ginsparg-Wilson relation) are briefly recalled and the exact cancellation of the gauge anomaly, at any fixed value of the lattice spacing and for any compact gauge group, is then proved rigorously through a recursive procedure.