Generalized Symmetries of the Graviton

In this talk we discuss the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by ring-like operators. As for the Maxwell field, we find a set of “electric” and a dual set of “magnetic” topological operators and compute their algebra. The associated electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a 3d CFT. This implies that the generalized symmetry is charged under space-time symmetries, and it provides a bridge between linearized gravity and the tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.