Generalized Symmetries of the Graviton

TL;DR

The paper identifies generalized symmetries of linearized gravity in four dimensions by constructing gauge-invariant, nonlocal topological operators that violate Haag duality in ring-like regions. It develops a gauge-invariant electric-magnetic formulation with $E_{ij}$ and $B_{ij}$, derives their algebra, and shows a 20-dimensional abelian symmetry group $\mathbb{R}^{10}\times (\mathbb{R}^{10})^*$, with graviton-specific charges carrying Lorentz indices. The resulting commutators reveal a graviton-topology structure that parallels Maxwell theory but with space-time symmetry charges and links to fracton tensor gauge theories. The discussion argues that completing the graviton theory within relativistic QFT may require breaking spacetime symmetries, aligning with fracton-inspired constructions and highlighting tensions with Coleman-Mandula and Weinberg-Witten constraints.

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.

Figures (6)

• Figure 1: Possible choices $\Sigma$ and $\Sigma'$ for fixed $\Gamma$.
• Figure 2: The ring-like regions $R$ and $\tilde{R}$ are the support of the currents $J(x)$ and $\tilde{J}(x)$.
• Figure 3: Example of the integration surface $\Sigma$. Here we use coordinates $(x_1,x_2,x_3)$ with the surface $\Sigma$ being orthogonal to $x_3$.
• Figure 4: Setup of a curve that defines a line operator
• Figure 5: Setup of the curves corresponding to a finite Wilson strip (left) and the associated infinitesimal limit or line operator (right).