TY - JOUR

T1 - Domain wall fermion and CP symmetry breaking

AU - Fujikawa, Kazuo

AU - Suzuki, Hiroshi

PY - 2003

Y1 - 2003

N2 - 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 q̄ together with Pauli-Villars fields Q and Q̄ are utilized. It is shown that this domain wall representation in the infinite flavor limit N=∝ 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.

AB - 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 q̄ together with Pauli-Villars fields Q and Q̄ are utilized. It is shown that this domain wall representation in the infinite flavor limit N=∝ 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.

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U2 - 10.1103/PhysRevD.67.034506

DO - 10.1103/PhysRevD.67.034506

M3 - Article

AN - SCOPUS:0037300027

VL - 67

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 3

M1 - 034506

ER -