A geometrical interpretation of parity violation in gravity with torsion

TL;DR

This paper introduces a geometric approach to incorporate parity violation in gravity with torsion by modifying the affine connection to include a pseudo-tensorial component, enabling parity-violating terms in matter field Lagrangians.

Contribution

It presents a novel geometric method to derive parity-violating terms in gravitational actions with torsion by modifying the affine connection.

Findings

Parity-violating terms can be derived from geometry itself.

A consistent method for including parity violation in matter field Lagrangians.

The approach applies to all matter fields with spin in torsioned spacetime.

Abstract

In a space-time with torsion, the action for the gravitational field can be extended with a parity-violating piece. We show how to obtain such a piece from geometry itself, by suitably modifying the affine connection so as to include a pseudo-tensorial part. A consistent method is thus suggested for incorporating parity-violation in the Lagrangians of all matter fields with spin in a space-time background with torsion.