Domain wall fermion and CP symmetry breaking

TL;DR

This paper investigates the CP symmetry properties of domain wall fermions in lattice chiral gauge theories, highlighting topological obstructions and proposing a modified CP transformation consistent with Ginsparg-Wilson fermions.

Contribution

It demonstrates the limitations of domain wall fermions in preserving CP symmetry and introduces a modified CP transformation aligned with Ginsparg-Wilson fermions.

Findings

CP symmetry conflicts with lattice chiral gauge theory in the infinite flavor limit

Modified CP transformation can preserve chiral action in the Ginsparg-Wilson framework

CP breaking may be a topological obstruction in lattice formulations

Abstract

We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables $q$ and $\bar q$ together with Pauli-Villars fields $Q$ and $\bar Q$ are utilized. It is shown that this domain wall representation in the infinite flavor limit $N=\infty$ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing $a$. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.