The Anomaly Inflow of the domain-wall fermion in odd dimension

In 1985, Callan and Harvey showed a view of gauge anomaly as a missing current into an extra-dimension, and the total contribution, including the Chern-Simons current in the bulk, is conserved. However in their computation, the edge and bulk contributions are separately evaluated and their cross correlations, which should be relevant at boundary, are simply ignored. This issue has been solved in many approaches. In this work, we revisit this issue with a complete set of eigenstates of free domain-wall Hamiltonian and give the systematic evaluation, easy to take in the higher mass correction and extend to the higher dimension.