Weyl and ghost fermions on the lattice

TL;DR

This paper explores a novel lattice formulation that allows Weyl fermions by relaxing hypercubic symmetry, clarifying the doubling problem and potential implications for lattice computations.

Contribution

It proposes a new approach to formulate Weyl fermions on the lattice by sacrificing hypercubic symmetry, addressing the doubling problem.

Findings

Clarifies the relation between the Nielsen-Ninomiya theorem and fermion doubling

Introduces a lattice theory with a single Weyl fermion and additional Dirac particles

Discusses potential impact on future lattice computations

Abstract

Nielsen-Ninomiya theorem forbids Weyl fermions on the lattice which respect the full hypercubic symmetry. By giving up this assumption in a specific way, it is possible to formulate a lattice theory with a single Weyl fermion in four dimensions and a sextet of Dirac particles in two dimensions. This way, the meaning of the theorem in relation to the doubling problem on the lattice is clarified. Whether the proposal will be suited for future lattice computations will depend on the effects the extra particles will have in the interacting theory.