Edge states and the $\eta$ invariant

Abstract

We propose a relation between the $\eta$ invariant on a manifold with boundary, the $\eta$ invariants of edge states, and the $\eta$ 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.

8 pages, v2: minor changes, a reference added

References in corpus (6)

• The Casimir effect with quantized charged spinor matter in background magnetic field
• Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
• Spectral asymmetry on the ball and asymptotics of the asymmetry kernel
• Non-topological fractional fermion number in the Jackiw-Rossi model
• Boundary conditions for the quantum Hall effect
• Anomaly inflow for local boundary conditions

Cited by in corpus (1)

• Vortex Fractional Fermion Number through Heat Kernel methods and Edge States