Gravitation and Duality Symmetry

TL;DR

This paper explores the duality symmetry in gravitation within teleparallel gravity, identifying a special self-dual theory where fermionic interactions become chiral, potentially aiding in quantum gravity renormalization.

Contribution

It generalizes the Hodge dual to soldered bundles and introduces a self-dual teleparallel gravity theory with unique fermionic interaction properties.

Findings

Gravitation generally lacks dual symmetry.

A self-dual teleparallel gravity exhibits chiral fermionic interactions.

This theory may be more suitable for renormalization than existing models.

Abstract

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than teleparallel gravity or general relativity.