Generalizations of the Nieh-Yan topological invariant

TL;DR

This paper introduces new four-dimensional topological invariants that extend the Nieh-Yan invariant by constructing $SO(4,1)$ and $SO(5)$ connections from lower symmetry connections and tensor forms, broadening the scope of topological invariants.

Contribution

It presents a systematic method to generate new topological invariants in four dimensions that generalize the Nieh-Yan form, including explicit expressions and special cases.

Findings

New topological invariants in four dimensions derived.

Explicit formulas for the invariants provided.

Nieh-Yan form identified as a special case.

Abstract

We report new topological invariants in four dimensions that are generalizations of the Nieh-Yan topological invariant. The new topological invariants are obtained through a systematic method along the lines of the one used to get the Nieh-Yan form, but involving an $SO(4,1)$ [$SO(5)$] connection constructed out from an $SO(3,1)$ [$SO(4)$] connection and three $SO(3,1)$ [$SO(4)$] tensor $1$-forms. We give explicit expressions of the new 4-forms that give rise to the new topological invariants for particular choices of these 1-forms and show that the Nieh-Yan form arises as a particular case.