Gauging generalised symmetries in linear gravity

TL;DR

This paper explores the generalized symmetries in linear gravity, identifying their structure, how to gauge them, and analyzing the anomalies that arise, especially those related by gravitational duality.

Contribution

It systematically characterizes the 1-form and (d-3)-form symmetries in linear gravity, introduces a method to gauge these symmetries, and analyzes the associated 't Hooft anomalies.

Findings

Certain symmetries can be interpreted as Noether currents.

A systematic method for gauging these symmetries is developed.

Mixed 't Hooft anomalies obstruct simultaneous gauging of some symmetry pairs.

Abstract

The theory of a free spin-2 field on Minkowski spacetime has 1-form and $(d-3)$-form symmetries associated with conserved currents formed by contractions of the linearised Riemann tensor with conformal Killing-Yano 2-forms. We show that a subset of these can be interpreted as Noether currents for specific shift symmetries of the graviton that involve a Killing vector and a closed 1-form parameter. We give a systematic method to gauge these 1-form symmetries by coupling the currents to background gauge fields and introducing a particular set of counter-terms involving the background fields. The simultaneous gauging of certain pairs of 1-form and $(d-3)$-form symmetries is obstructed by the presence of mixed 't Hooft anomalies. The anomalous pairs of symmetries are those which are related by gravitational duality. The implications of these anomalies are discussed.