On Majorana fermions on the lattice

TL;DR

This paper investigates the challenges of formulating massless Majorana fermions with chiral Yukawa couplings on the lattice, revealing topological obstructions and proposing a chirally invariant lattice action with a Pfaffian path integral.

Contribution

It identifies topological obstructions specific to Majorana fermions on the lattice and constructs a chirally invariant action using the Pfaffian of the Dirac operator.

Findings

Topological obstructions are linked to the Nielsen-Ninomiya theorem.

A chirally invariant lattice action for Majorana fermions is constructed.

The path integral is expressed as the Pfaffian of the Dirac operator.

Abstract

The construction of massless Majorana fermions with chiral Yukawa couplings on the lattice is considered. We find topological obstructions tightly linked to those underlying the Nielsen-Ninomiya no-go theorem. In contradistinction to chiral fermions the obstructions originate only from the combination of the Dirac action and the Yukawa term. These findings are used to construct a chirally invariant lattice action. We also show that the path intgral of this theory is given by the Pfaffian of the corresponding Dirac operator.