Hamiltonian approach to the torsional anomalies and its dimensional ladder
Abstract
Torsion can cause various anomalies in various dimensions, including the (3+1)-dimensional [(3+1)D] Nieh-Yan anomaly, the (2+1)D Hughes-Leigh-Fradkin (HLF) parity anomaly, and the (3+1)D, (1+1)D chiral energy-momentum anomaly. We study these anomalies from the Hamiltonian approach. We derive the (1+1)D chiral energy-momentum anomaly from the single-body Hamiltonian. We then show how other torsional anomalies can be related to the (1+1)D chiral energy-momentum anomaly in a straightforward way. Finally, the Nieh-Yan anomaly and the (3+1)D chiral energy-momentum anomaly are obtained from the parity anomaly and the HLF effective action, respectively. Hence, we have constructed the dimensional ladder for the torsional anomalies from the single-body Hamiltonian picture.
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