Generalized Symmetries of the Graviton

TL;DR

This paper characterizes the generalized symmetries of free graviton theory in four dimensions, revealing topological operators that violate Haag duality and exploring their algebra and physical implications.

Contribution

It identifies and analyzes the gauge-invariant topological operators in linearized gravity, including their algebra and relation to stress tensor constraints, extending symmetry understanding in gravitational theories.

Findings

Identified electric and magnetic topological operators in linearized gravity.

Computed the algebra of these operators, revealing a group 0.

Compared linearized gravity symmetries with tensor gauge theories in condensed matter.

Abstract

We find the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality in ring-like regions. As expected from general QFT grounds, we find a set of "electric" and a dual set of "magnetic'" topological operators and compute their algebra. To do so, we describe the theory using phase space gauge-invariant electric and magnetic dual variables constructed out of the curvature tensor. Electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a $3d$ CFT. The constraints give place to a group $\mathbb{R}^{20}$ of topological operators that are charged under space-time symmetries. Finally, we discuss similarities and differences between linearized gravity and tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.