Manifestly Gauge Covariant Treatment of Lattice Chiral Fermions. II

TL;DR

This paper introduces a new lattice formulation for chiral fermions that maintains gauge invariance and avoids species doublers, aligning with continuum regularization principles.

Contribution

It presents a gauge covariant lattice approach for chiral fermions that ensures gauge invariance and eliminates species doublers, advancing lattice gauge theory methods.

Findings

Species doublers do not appear in the formulation.

The real part of the effective action is half that of Dirac-Wilson fermions and gauge invariant.

For real gauge representations, the imaginary part vanishes, ensuring exact gauge invariance.

Abstract

We propose a new formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint which is a lattice analogue of the gauge anomaly free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.