Index Theorems and Domain Walls

Understand

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.