A no-go theorem for the Majorana fermion on a lattice

TL;DR

This paper proves a no-go theorem showing that under certain assumptions, a doubler-free lattice action for a single Majorana fermion cannot exist in specific dimensions, highlighting fundamental limitations in lattice fermion formulations.

Contribution

It formulates a variant of the Nielsen--Ninomiya no-go theorem specifically for Majorana fermions in certain dimensions, establishing fundamental constraints.

Findings

Doubler-free lattice actions for Majorana fermions are impossible in 8k and 8k+1 dimensions under the assumptions.

The theorem extends the understanding of lattice fermion formulations and their limitations.

Provides a theoretical foundation for future lattice fermion research in high-energy physics.

Abstract

A variant of the Nielsen--Ninomiya no-go theorem is formulated. This theorem states that, under several assumptions, it is impossible to write down a doubler-free Euclidean lattice action of a single Majorana fermion in $8k$ and $8k+1$ dimensions.