Gauge-invariant charges of the dual graviton

TL;DR

This paper explores gauge-invariant conserved charges in dual formulations of linearized gravity, revealing their topological nature and addressing issues in non-trivial topologies.

Contribution

It introduces gauge-invariant conserved charges for the dual graviton theory, providing local expressions and clarifying their role as symmetry generators.

Findings

Gauge-invariant charges can be constructed with improvement terms.

Charges serve as topological operators generating genuine symmetries.

Dual graviton charges relate to ADM charges as magnetic counterparts.

Abstract

The free graviton theory given by linearising Einstein's theory has a dual formulation in terms of a dual graviton field. The dual graviton theory has two gauge invariances giving rise to two conserved charges, while the ADM charges of the graviton theory become magnetic charges for the dual graviton theory. These charges can be ill-defined in topologically non-trivial settings and we find improvement terms that can be added to these to give gauge-invariant conserved charges. These gauge-invariant charges, which have local expressions in both the graviton and dual graviton formulation, give topological operators of the theory that should be considered as the generators of the genuine symmetries of the theory.