The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators

Abstract

We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.

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• Worldline approach for spinor fields in manifolds with boundaries
• Mod-two APS index and domain-wall fermion
• Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase
• Anomaly inflow for local boundary conditions
• $K$-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators
• Index Theorem for Domain Walls
• Understanding the index theorems with massive fermions
• Localization of a $K{O}^{\ast }(\text{pt})$-valued index and the orientability of the $Pi{n}^{-}(2)$ monopole moduli space