# A Possible Lattice Chiral Gauge Theory

## TL;DR

This paper investigates a lattice formulation of an $SU_L(2) imes U_R(1)$ chiral gauge theory, demonstrating decoupling of doublers, free spectator fermions, and discussing conditions for chiral fermion emergence and anomaly consistency.

## Contribution

It presents a lattice model with large multifermion coupling that maintains chiral gauge symmetry and decouples doublers without spontaneous symmetry breaking, advancing lattice chiral gauge theory understanding.

## Key findings

- Doublers are decoupled as massive Dirac fermions.
- Spectator fermion remains free and non-interacting.
- Conditions for emergence of chiral fermions are discussed.

## Abstract

We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral gauge theory on a lattice with a large multifermion coupling $1\ll g_2 < \infty$. It is shown that no spontaneous symmetry breaking occurs; the ``spectator'' fermion $\psi_R(x)$ is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral gauge symmetry. Whether right-handed three-fermion states disappear and chiral fermions emerge in the low-energy limit are discussed. Provided right-handed three-fermion states disappear, we discuss the chiral gauge coupling, Ward identities, the gauge anomaly and anomalous $U_L(1)$ global current within the gauge-invariant prescription of renormalization of the gauge perturbation theory.