Domain wall fermion and CP symmetry breaking

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.

33 pages. Note added and a new reference were added. Phys. Rev.D (in press)

References in corpus (5)

• Supersymmetry on the lattice and the Leibniz rule
• Lattice chiral symmetry, Yukawa couplings and the Majorana condition
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Ginsparg-Wilson operators and a no-go theorem
• CP breaking in lattice chiral gauge theories

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• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• CP, T and CPT in the non-perturbative formulation of chiral gauge theories
• Majorana fermions and CP-invariance of chiral gauge theories on the lattice
• CP symmetry and lattice chiral gauge theories