Duality for symmetric second rank tensors. II. The linearized gravitational field

TL;DR

This paper develops a dual formulation of linearized gravity using a parent Lagrangian approach, revealing a gauge-symmetric theory with a symmetric tensor and auxiliary field, and explores its physical implications.

Contribution

It introduces a dual theory for linearized gravity with an enlarged gauge symmetry, extending previous massive spin-two duality methods to the zero mass case.

Findings

Dual theory described by a symmetric tensor and auxiliary field

Enlarged gauge symmetry with partial gauge fixing

Zero mass dual theory contains only a spin-zero excitation

Abstract

The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples illustrating the general procedure and the physical interpretation of the dual fields. The zero mass case of the massive theory dual to the massive spin-two theory is also examined, but we show that it only contains a spin-zero excitation.