Gravitons and a complex of differential operators

TL;DR

This paper introduces a novel off-shell formulation of gravity using a complex of differential operators, leading to a simple Lagrangian for gravitons applicable on certain four-dimensional manifolds.

Contribution

It presents a new Lagrangian for gravitons based on a complex of differential operators, extending the simplicity of on-shell gravity to off-shell scenarios.

Findings

A simple off-shell Lagrangian for gravitons is constructed.

The formulation is valid on half-conformally flat four-dimensional manifolds.

The approach parallels Maxwell's theory using a different complex.

Abstract

Gravity is now understood to become simple on-shell. We sketch how it becomes simple also off-shell, when reformulated appropriately. Thus, we describe a simple Lagrangian for gravitons that makes use of a certain complex of differential operators. The Lagrangian is constructed analogously to that of Maxwell's theory, just using a different complex. The complex, and therefore also our description of gravitons, makes sense on any half-conformally flat four-dimensional manifold.