Manifest duality and Lorentz covariance for linearised gravity as edge modes

TL;DR

This paper introduces a Lorentz covariant and duality-symmetric formulation of linearised gravity in four dimensions, using a five-dimensional topological field approach and boundary reduction.

Contribution

It presents the first manifestly Lorentz covariant and duality-symmetric formulation of linearised gravity, connecting four-dimensional fields to five-dimensional topological theories.

Findings

Formulation treats electric-magnetic duality on equal footing.

Uses five-dimensional topological field theory to derive four-dimensional action.

Establishes a boundary reduction procedure for the formulation.

Abstract

We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that four-dimensional linearised gravity belongs to a class of singleton representations of the four-dimensional conformal algebra $\mathfrak{so}(2,4)$. Our key insight is viewing this algebra as the isometry of $\text{AdS}_5$ and realising the massless spin-2 field as an edge mode of a five-dimensional topological field taking values in a specific finite-dimensional representation of $\mathfrak{so}(2,4)$. The desired four-dimensional action is then found by a covariant boundary reduction procedure.