The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries

Author(s)

Erdmenger, Johanna ; Matthaiakakis, Ioannis ; Meyer, Rene ; Vassilevich, Dmitri

• Document type: Journal article
• Source: Journal of High Energy Physics; v. N/A, n. 12, p. 21-pg., 2024-12-19.

Abstract

There exists a long-standing debate regarding the torsion contribution to the 4d chiral anomaly of a Dirac fermion. Central to this debate is the Nieh-Yan anomaly, which has been considered ill-defined and a regularization artifact. Using a heat-kernel approach, we examine the relationship between the Dirac operator index, the Nieh-Yan invariant and the torsional anomaly. We show the Nieh-Yan invariant vanishes on spacetimes without boundaries, if the Dirac index is well-defined. In the known examples of non-vanishing Nieh-Yan invariant on manifolds without boundaries, the heat kernel expansion breaks down, making the index ill-defined. Finally, for finite boundaries we identify several finite bulk and boundary anomaly terms, alongside bulk and boundary Nieh-Yan terms. We construct explicit counterterms that cancel the Nieh-Yan terms and argue that the boundary terms give rise to a torsional anomalous Hall effect. Our results emphasize the importance of renormalization conditions, as these can affect the non-thermal Nieh-Yan anomaly coefficients. In addition, we demonstrate that anomalous torsional transport may arise even without relying on the Nieh-Yan invariant. (AU)

• FAPESP's process: 21/10128-0 - Quantum field theory under the influence of external conditions
• Grantee: Dmitry Vasilevich
• Support Opportunities: Research Projects - Thematic Grants