Dual linearized gravity in arbitrary dimensions

Abstract

We construct a dual formulation of linearized gravity in a first-order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field in a frame-like formulation. We obtain in d dimensions the dual Lagrangian in a closed form in terms of the field strength of the dual frame-like field. Next, by coupling a source with the (linear) Riemann tensor in d dimensions, a dual generating functional is obtained. Using this an operator mapping between (linear) Riemann tensor and Riemann tensor corresponding to the dual field is derived and we also discuss the exchange of equations of motion and Bianchi identity.