Manifest electric-magnetic duality in linearized conformal gravity

TL;DR

This paper presents a duality-symmetric Hamiltonian formulation of linearized conformal gravity, introducing dual potentials and a twisted self-duality approach to better understand its fundamental symmetries.

Contribution

It develops a manifestly duality-symmetric action for linearized conformal gravity using Hamiltonian methods and dual potentials, which is a novel approach in the field.

Findings

Dual potentials are introduced as independent variables.

The action exhibits duality as rotations in metric and extrinsic curvature spaces.

A twisted self-duality formulation of equations of motion is established.

Abstract

We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations of motion requiring the formal treatment of the three-dimensional metric perturbation and the extrinsic curvature as independent dynamical variables. The constraints are solved in terms of two symmetric potentials that are interpreted as a dual three-dimensional metric and a dual extrinsic curvature. The action principle can be written in terms of these four dynamical variables, duality acting as simultaneous rotations in the respective spaces spanned by the three-dimensional metrics and the extrinsic curvatures. A twisted self-duality formulation of the equations of motion is also provided.