Lattice Regularization of Gauge Theories Without Loss of Chiral Symmetry

TL;DR

This paper introduces a lattice regularization method for gauge theories that preserves chiral flavor symmetries without fermion doubling, enabling analytical studies of symmetry and anomaly phenomena.

Contribution

A novel lattice regularization scheme that maintains chiral symmetries and avoids fermion doubling, with potential applications in theoretical analysis.

Findings

Preserves all anomaly-free chiral flavor symmetries.

Avoids fermion doubling in lattice gauge theories.

Allows study of symmetry breaking and anomalies.

Abstract

A lattice regularization procedure for gauge theories is proposed in which fermions are given a special treatment such that all chiral flavor symmetries that are free of Adler-Bell-Jackiw anomalies are kept intact. There is no doubling of fermionic degrees of freedom. A price paid for this feature is that the number of fermionic degrees of freedom per unit cell is still infinite, although finiteness of the complete functional integrals can be proven (details are outlined in an Appendix). Therefore, although perhaps of limited usefulness for numerical simulations, our scheme can be applied for studying aspects such as analytic convergence questions, spontaneous symmetry breakdown and baryon number violation in non-Abelian gauge theories.