CP symmetry and lattice chiral gauge theories

TL;DR

This paper investigates the challenge of maintaining CP symmetry in lattice chiral gauge theories, revealing that CP symmetry is not manifestly preserved in certain formulations and identifying where CP breaking effects occur.

Contribution

The paper analyzes CP symmetry in lattice chiral gauge theories, showing that it is not manifestly preserved with Ginsparg-Wilson operators and pinpointing the origin of CP breaking effects.

Findings

CP symmetry is not manifestly implemented in Ginsparg-Wilson lattice formulations.

The analysis identifies specific points where CP breaking effects appear.

The study clarifies the relationship between lattice chiral gauge theories and CP symmetry.

Abstract

The CP symmetry is a fundamental discrete symmetry in chiral gauge theory. Therefore this symmetry is expected to be kept also on the lattice. However, it has been pointed out by Hasenfratz that the chiral fermion action in Luscher's formulation of lattice chiral gauge theory is not invariant under CP transformation. In this thesis, we first review the method of constructing chiral gauge theory on the lattice. Then we generalize the analysis of Hasenfratz and show that CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator under rather general assumptions for chiral projection operators. We next calculate the fermion generating functional and precisely identify where the effects of this CP breaking appear in this formulation. The basics of lattice gauge theory are briefly summarized in Appendix.A.