The Topological Structure of Nieh-Yan Form and Chiral Anomaly in Spaces with Torsion

TL;DR

This paper explores the topological properties of the Nieh-Yan form and its relation to chiral anomaly in spaces with torsion, extending the analysis to higher dimensions and identifying torsion's contributions to anomalies.

Contribution

It provides a detailed decomposition of the Nieh-Yan form in 4D and generalizes it to 2^d-dimensional manifolds, analyzing torsion's role in chiral anomalies.

Findings

Decomposition of Nieh-Yan form in 4D using spin connection

Generalization of Nieh-Yan form to 8D and higher dimensions

Identification of torsion contributions to chiral anomaly from zeroes of certain fields

Abstract

The topological structure of the Nieh-Yan form in 4-dimensional manifold is given by making use of the decomposition of spin connection. The case of the generalized Nieh-Yan form on $2^d$-dimensional manifold is discussed with an example of 8-dimensional case studied in detail. The chiral anomaly with nonvanishing torsion is studied also. The further contributions from torsional part to chiral anomaly are found coming from the zeroes of some fields under pure gauge condition.