Index Theorems and Domain Walls

Abstract

The Atiyah-Patodi-Singer (APS) index theorem relates the index of a Dirac operator to an integral of the Pontryagin density in the bulk (which is equal to global chiral anomaly) and an $\eta$ invariant on the boundary (which defines the parity anomaly). We show that the APS index theorem holds for configurations with domain walls that are defined as surfaces where background gauge fields have discontinuities.

11+1 pages, v2: a reference added

References in corpus (4)

• Gravitational parity anomaly with and without boundaries
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• 't Hooft anomalies and boundaries
• Parity Anomaly and Duality Web

Cited by in corpus (14)

• Holographic BCFT with Dirichlet Boundary Condition
• The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
• Casimir Effect, Weyl Anomaly and Displacement Operator in Boundary Conformal Field Theory
• Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line
• Atiyah-Patodi-Singer Index Theorem for Domain Walls
• Anomaly and Superconnection
• Interface Conformal Anomalies
• Note on anomalous currents for a free theory
• 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
• Index Theorem for Domain Walls
• Understanding the index theorems with massive fermions
• Remark on the synergy between the heat kernel techniques and the parity anomaly