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

2025/11/19 by Harun Basmaci, Basmaci, Harun, Hasan Özgür Çıldıroğlu +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2511.15765

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

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.

Citations

• Entanglement and Effective Field Theories
• Understanding the chiral and parity anomalies without Feynman diagrams
• Quantal phase factors accompanying adiabatic changes
• Significance of Electromagnetic Potentials in the Quantum Theory

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• Parity Anomalous Semimetal with Minimal Conductivity Induced by an In-Plane Magnetic Field
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• Anomaly and Thermodynamics for 2D Spinors in the Aharonov--Bohm Gauge Field