This research aims to analyze the integrability condition of the chiral determinant of 4D overlap fermions and construct lattice chiral gauge theories. We formulate the integrability condition with 5D and 6D lattice domain-wall fermions. Our formulation parallels the recent cobordism classification of the global ‘t Hooft anomaly using the eta-invariant based on the Dai-Freed theorem and the Atiya-Patodi-Singer index theorem in the continuum theory.
Nobuyuki Matsumoto