On the chiral anomaly in non-Riemannian spacetimes

TL;DR

This paper explores the role of the Nieh-Yan form in non-Riemannian spacetimes, revealing its significance in classical and quantum theories of gravity with torsion, challenging previous assumptions.

Contribution

It demonstrates the appearance of the Nieh-Yan form in both classical Einstein-Cartan-Dirac theory and quantum heat kernel approaches, clarifying its fundamental role.

Findings

Nieh-Yan form appears in classical Einstein-Cartan-Dirac theory

Nieh-Yan form emerges in quantum heat kernel analysis

Challenges previous assumptions about the form's significance

Abstract

The translational Chern-Simons type three-form coframe torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan four-form. Following Chandia and Zanelli, two spaces with non-trivial translational Chern-Simons forms are discussed. We then demonstrate, firstly within the classical Einstein-Cartan-Dirac theory and secondly in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.