Duality in linearized gravity

TL;DR

This paper demonstrates that duality transformations in linearized gravity can be extended to the dynamical fields, making them symmetries of the action through the use of superpotentials, with a structure similar to Maxwell theory.

Contribution

It introduces superpotentials for linearized gravity that enable duality transformations to be symmetries of the action, not just the equations of motion.

Findings

Duality transformations can be extended to the action in linearized gravity.

Superpotentials are symmetric tensors that serve as basic dynamical fields.

The canonical generator of duality has a Chern-Simons-like structure.

Abstract

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two "superpotentials", one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons like structure, as in the Maxwell case.