A lattice implementation of the eta-invariant and effective action for chiral fermions on the lattice

Abstract

We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained.

arXiv comment38 pages, LaTeX, revised version

References in corpus (2)

• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion

Cited by in corpus (5)

• Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance