The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

Abstract

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five dimensional lattice domain wall fermions. In the case that the target continuum theory contains $4n$ chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.

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Cited by in corpus (18)

• Lattice Chiral Gauge Theories
• Anomaly Cancellation Condition in Lattice Gauge Theory
• Lattice Formulation of the Standard Model
• Lattice Chiral Fermions
• The Standard Model from a New Phase Transition on the Lattice
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Interpolation of Non-abelian Lattice Gauge Fields
• A Lattice Formulation of Chiral Gauge Theories
• The overlap is not a waveguide
• Perturbative study for domain-wall fermions in 4+1 dimensions
• Domain-wall fermions with $U(1)$ dynamical gauge fields
• Progress in lattice chiral gauge theories
• Chiral zero modes on the domain-wall model in 4+1 dimensions
• Why the overlap formula does not lead to chiral fermions
• Manifestly Gauge Covariant Treatment of Lattice Chiral Fermions. II
• Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap
• Gribov Copy and Complex Phase of Chiral Determinant
• Desperately Seeking Chiral Fermions