A deformation of the Curtright action

TL;DR

This paper introduces a novel, non-local deformation of the Curtright action for a mixed symmetry tensor field, derived as a dual to linearized gravity on a de Sitter background, overcoming previous limitations.

Contribution

It presents a new non-local action for the (2,1) tensor field, constructed via duality and two-potential formalism, breaking previous no-go constraints.

Findings

The deformed action is spatially non-local.

It is dual to linearized gravity around de Sitter space.

Space-time covariance is not manifest in the new formulation.

Abstract

We present a deformation of the action principle for a free tensor field of mixed symmetry (2,1) --the Curtright action, a dual formulation of five-dimensional linearized gravity. It is constructed as the dual theory of the Einstein-Hilbert action linearized around a de Sitter background, and its derivation relies on the use of the two-potential formalism as an intermediate step. The resulting action principle is spatially non-local and space-time covariance is not manifest, thus overcoming previous no-go results.