Parity anomalies in 2+1-dimensional Aharonov-Bohm type configurations

TL;DR

Problem: parity anomalies in $2+1$-D AB-type configurations generate AB-type and AC-type topological phases. Approach: apply the Fujikawa path-integral method, leveraging the APS framework, to derive anomaly terms and induced currents in AB and AC setups. Key findings: AB phase $M = e Phi$ and spin-dependent AC phase $M = s mu lambda$, with divergence-free induced currents. Significance: unifies AB/AC phenomena within a quantum-field-theoretic parity anomaly picture and suggests extensions to He-McKellar-Wilkens and Dual AB phases.

Abstract

We demonstrate that Dirac fermions in 2+1 dimensions, coupled to Abelian gauge fields in multiply-connected regions, exhibit a parity anomaly that directly manifests as Aharonov-Bohm (AB) type topological phases. Using the Fujikawa method, we show that this anomaly reproduces both the AB phase and the spin-dependent Aharonov-Casher (AC) phase. We explicitly calculate the induced topological currents, establishing that their characteristic divergence-free form provides a direct signature of this parity-anomalous topological phase.