On Torsion and Nieh-Yan Form

TL;DR

This paper systematically constructs torsion-induced Chern-Simons and Nieh-Yan forms using Chern-Weil theory, explores their properties, and extends the construction to higher dimensions.

Contribution

It provides a systematic method for constructing Nieh-Yan forms in various dimensions and analyzes their integral properties.

Findings

Nieh-Yan forms vanish upon integration on compact manifolds without boundary.

Constructed generalized N-Y forms in 4n dimensions.

Demonstrated the relation between torsion, Chern-Simons, and N-Y forms.

Abstract

Using the well-known Chern-Weil formula and its generalization, we systematically construct the Chern-Simons forms and their generalization induced by torsion as well as the Nieh-Yan (N-Y) forms. We also give an argument on the vanishing of integration of N-Y form on any compact manifold without boundary. A systematic construction of N-Y forms in D=4n dimension is also given.