Consistent deformations of dual formulations of linearized gravity: A no-go result

TL;DR

This paper investigates the possibility of consistent deformations in the dual formulation of linearized gravity, establishing the rigidity of gauge algebra and proving a no-go theorem for certain interactions.

Contribution

It provides a systematic analysis showing the impossibility of certain local deformations in the dual gravity formulation, highlighting its rigidity.

Findings

Rigidity of the Abelian gauge algebra.

No-go theorem for interactions with at most two derivatives.

Systematic investigation of deformations in dual gravity formulations.

Abstract

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of length 1) are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields.