Gauging generalised symmetries in linear gravity

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.