Torsion, Parity-odd Response and Anomalies in Topological States

Understand

We study the response of a class of topological systems to electromagnetic and gravitational sources, including torsion and curvature.

• By using the technology of anomaly polynomials, we derive the parity-odd response of a massive Dirac fermion in $d=2+1$ and $d=4+1$, which provides a simple model for a topological insulator.
• We discuss the covariant anomalies of the corresponding edge states, from a Callan-Harvey anomaly-inflow, as well as a Hamiltonian spectral flow point of view.
• We also discuss the applicability of our results to other systems such as Weyl semi-metals.