Thermal response of the Nieh-Yan term

TL;DR

This paper reinterprets the Nieh-Yan anomaly holographically, showing it stems from a breakdown of duality relations in fermion bilinears, with a distinct temperature-dependent axial response.

Contribution

It provides a new holographic perspective on the Nieh-Yan anomaly, clarifying its physical origin and differentiating it from the chiral vortical effect.

Findings

Axial response exhibits a $T^2$ dependence.

The U(1) axial symmetry remains unbroken.

Torsion-induced axial transport decouples spin and axial charge.

Abstract

We reinterpret the Nieh-Yan (NY) anomaly using holography, finding that the U(1) axial symmetry remains unbroken and the axial current coupling to an external gauge field is conserved. Instead, the anomaly arises from a breakdown of Hodge duality relations between fermion bilinears due to symmetry constraints on one-form currents. We show that the axial response associated with the NY term is distinct from the chiral vortical effect and exhibits a characteristic $T^2$ dependence. Torsion-induced axial transport decouples spin and axial charge dynamics, thereby clarifying the physical significance of the NY anomaly and motivating further field-theoretic and holographic studies.