Dual Linearised Gravity in Arbitrary Dimensions

TL;DR

This paper develops a dual formulation of linearised gravity in arbitrary dimensions using a first order tetrad formalism, deriving a dual Lagrangian and operator mappings in a path integral framework.

Contribution

It introduces a novel dual formulation of linearised gravity in arbitrary dimensions within the first order tetrad formalism, including explicit dual Lagrangian and operator mappings.

Findings

Derived the dual Lagrangian in closed form for arbitrary dimensions.

Established an operator mapping between Riemann tensors of original and dual fields.

Discussed the exchange of equations of motion and Bianchi identities in the dual framework.

Abstract

We construct dual formulation of linearised gravity in 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 $\Phi_{[\nu_{1}\nu_{2}...\nu_{d-3}]\nu}$ in {\it frame-like} formulation. We obtain in d-dimensions the dual Lagrangian in a closed form in terms of field strength of the dual frame-like field. Next by coupling a source with the (linear) Riemann tensor in d-dimensions, 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.