Duality-invariant bimetric formulation of linearized gravity

TL;DR

This paper presents a new bimetric formulation of linearized gravity that is explicitly invariant under electric-magnetic duality, featuring variables with clear geometric meaning but with a non-local spatial kinetic term.

Contribution

It introduces a duality-invariant bimetric formulation of linearized gravity using both metrics as fundamental variables, differing from prepotential approaches.

Findings

Kinetic term is non-local in space but local in time.

Hamiltonian is local in both space and time.

Variables are constrained by two Hamiltonian constraints.

Abstract

A formulation of linearized gravity which is manifestly invariant under electric-magnetic duality rotations in the internal space of the metric and its dual, and which contains both metrics as basic variables (rather than the corresponding prepotentials), is derived. In this bimetric formulation, the variables have a more immediate geometrical significance, but the action is non-local in space, contrary to what occurs in the prepotential formulation. More specifically, one finds that: (i) the kinetic term is non-local in space (but local in time); (ii) the Hamiltonian is local in space and in time; (iii) the variables are subject to two Hamiltonian constraints, one for each metric.