Gravity, dual gravity and A1+++

Abstract

We construct the nonlinear realisation of the semidirect product of the very extended algebra [Formula: see text] and its vector representation. This theory has an infinite number of fields that depend on a space–time with an infinite number of coordinates. Discarding all except the lowest level field and coordinates the dynamics is just Einstein’s equation for the graviton field. We show that the gravity field is related to the dual graviton field by a duality relation and we also derive the equation of motion for the dual gravity field.