Thermal response of the Nieh-Yan term

Abstract: We reinterpret the Nieh-Yan 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 also compute the thermal response of the Nieh-Yan term, revealing its characteristic $T^2$ dependence.