Y. Kikukawa, A lattice implementation of the eta-invariant and effective action for chiral Ginsparg-Wilson fermions, CHIN J PHYS, 38(3), 2000, pp. 583-593
We consider a lattice implementation of the eta-invariant, using the comple
x phase of the determinant of the simplified domain-wall fermion which coup
les to an interpolating five-dimensional gauge field. We clarify the relati
on to the effective action for chiral Ginsparg-Wilson fermions. A lattice e
xpression for the five-dimensional Chern-Simons term is obtained.