# Undoubled Chiral Fermions on a Lattice

## TL;DR

This paper demonstrates that a lattice formulation of an $SU_L(2) imes U_R(1)$ chiral theory can avoid fermion doubling and spontaneous symmetry breaking, maintaining chiral symmetry and producing a single chiral fermion in the continuum limit.

## Contribution

It introduces a lattice approach with strong multifermion coupling that successfully decouples doublers and preserves chiral symmetry without breaking it.

## Key findings

- Doublers are decoupled as massive Dirac fermions.
- The spectator fermion remains free and decoupled.
- A single chiral fermion persists in 1+1 dimensions.

## Abstract

We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral theory on the lattice with a strong multifermion coupling. It is shown that no spontaneous symmetry breaking occurs; the ``spectator'' fermion $\psi_R$ is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral symmetries. In 1+1 dimension, we show that the right-handed three-fermion state disappears at the threshold and an undoubled left-handed chiral fermion remains in the continuum limit.