Thermal response of the Nieh-Yan term

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.