Generalized Chern-Simons Modified Gravity in First-Order Formalism

TL;DR

This paper extends Chern-Simons modified gravity in the first-order formalism by incorporating the Nieh-Yan torsional invariant, resulting in a more general torsional theory with potential implications for gravitational anomalies.

Contribution

It introduces a generalized Chern-Simons gravity theory by adding the Nieh-Yan term, expanding the understanding of torsional effects in gravitational models.

Findings

Derived the effective theory with the Nieh-Yan term

Compared the generalized and original CS theories

Discussed implications of torsional topological terms

Abstract

We propose a generalization of Chern-Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences.