Generalised symmetries in linear gravity

TL;DR

This paper explores the extended symmetry structure of linearised gravity, revealing dual symmetries, conserved charges, and anomalies, and interprets gravitons as Nambu-Goldstone modes for these symmetries.

Contribution

It introduces a dual symmetry in linearised gravity, analyzes the algebra of conserved charges, and uncovers an obstruction to gauging both symmetries simultaneously.

Findings

Conserved charges form a centrally-extended algebra.

An obstruction exists to gauging both symmetries simultaneously.

Gravitons are interpreted as Nambu-Goldstone modes.

Abstract

Linearised gravity has a global symmetry under which the graviton is shifted by a symmetric tensor satisfying a certain flatness condition. There is also a dual symmetry that can be associated with a global shift symmetry of the dual graviton theory. The corresponding conserved charges are shown to satisfy a centrally-extended algebra. We discuss the gauging of these global symmetries, finding an obstruction to the simultaneous gauging of both symmetries which we interpret as a mixed 't Hooft anomaly for the ungauged theory. We discuss the implications of this, analogous to those resulting from a similar structure in Maxwell theory, and interpret the graviton and dual graviton as Nambu-Goldstone modes for these shift symmetries.