Edge states and the Invariant
Rodrigo Fresneda (Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo André, SP, Brazil); Lucas de Souza (Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo André, SP, Brazil); Dmitri Vassilevich (Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo André, SP, Brazil)
We propose a relation between the η invariant on a manifold with boundary, the η invariants of edge states, and the η invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary conditions we show that this relation holds whenever edge states are sufficiently well-localized near the boundary. As a by-product we show that the spectrum of edge modes for chiral bag boundary conditions is linear but bounded.