Speaker
Description
Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz.
But its extension to the system with boundary ( the so-called Atiyah-Patodi-Singer index theorem), which surprisingly plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and no lattice realization has been made so far.
In this work, we try to non-perturbatively define an alternative index from the lattice domain-wall fermion in 3+1 dimensions. We will show that this new index in the continuum limit, converges tothe Atiyah-Patodi-Singer index defined on a manifold with boundary, which coincides with the surface of the domain-wall.
