Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra

TL;DR

This paper extends the non-linear realisation of $A_1^{+++}$ to linearised gravity, deriving equations for higher dual fields and systematically identifying additional fields needed for dual gravity descriptions.

Contribution

It introduces a systematic method to find additional fields for dual gravity actions within the $A_1^{+++}$ framework and links them to the second fundamental representation.

Findings

Derived equations of motion for higher dual gravity fields.

Provided a systematic approach to identify additional fields.

Linked extra fields to the second fundamental representation of $A_1^{+++}$.

Abstract

The non-linear realisation based on $A_1^{+++}$ is known to describe gravity in terms of both the graviton and the dual graviton. We extend this analysis at the linearised level to find the equations of motion for the first higher dual description of gravity that it contains. We also give a systematic method for finding the additional fields beyond those in the non-linear realisation that are required to construct actions for all of the possible dual descriptions of gravity in the non-linear realisation. We show that these additional fields are closely correlated with the second fundamental representation of $A_1^{+++}\,$.