Lattice chiral symmetry, CP-violation and Majorana fermions

TL;DR

This paper examines the limitations of lattice fermions satisfying the Ginsparg-Wilson algebra, revealing conflicts with CP invariance and Majorana fermion definitions in chiral gauge theories.

Contribution

It demonstrates that a broad class of lattice fermions, including domain-wall fermions, cannot simultaneously maintain chiral symmetry, CP invariance, and proper Majorana fermion definitions.

Findings

Ginsparg-Wilson fermions conflict with CP invariance in chiral gauge theories

Majorana fermions cannot be consistently defined with chiral-symmetric Yukawa couplings on the lattice

Domain-wall fermions share the same fundamental conflicts

Abstract

A brief summary of lattice fermions defined by the general Ginsparg-Wilson algebra is first given. It is then shown that those general class of fermion operators have a conflict with CP invariance in chiral gauge theory and with the definition of Majorana fermions in the presence of chiral-symmetric Yukawa couplings. The same conclusion holds for the domain-wall fermion also.