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Gravity, Dual Gravity and A1+++
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We construct the non-linear realisation of the semi-direct product of the very extended algebra A1+++ and its vector representation. This theory has an infinite number of fields that depend on a spacetime 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.
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Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.
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