# A Lattice Chiral Theory with Multifermion Couplings

## TL;DR

This paper explores a lattice chiral theory with multifermion couplings, identifying a phase where chiral symmetry is preserved, doublers are decoupled, and the continuum limit may yield a chiral fermion, challenging previous beliefs.

## Contribution

It demonstrates a possible lattice phase with preserved chiral symmetry and decoupled doublers using multifermion couplings, contrary to common assumptions.

## Key findings

- No spontaneous symmetry breaking in the identified phase
- Doublers become massive Dirac fermions and decouple
- Normal mode of $ ext{psi}_L^i$ may be chiral in continuum limit

## Abstract

Analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory with multifermion couplings on a lattice, we find a possible region in the phase space of multifermion couplings, where no spontaneous symmetry breaking occurs, doublers are decoupled as massive Dirac fermions consistently with the $SU_L(2)\otimes U_R(1)$ chiral symmetry, the ``spectator'' fermion $\psi_R(x)$ is free mode, whereas the normal mode of $\psi^i_L(x)$ is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.