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Extended Lie derivatives and a new formulation of D=11 supergravity

Leonardo Castellani
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Abstract

Introducing an extended Lie derivative along the dual of A, the three-form field of d=11 supergravity, the full diffeomorphism algebra of d=11 supergravity is presented. This algebra suggests a new formulation of the theory, where the three-form field A is replaced by bivector B^{ab}, bispinor B^{αβ}, and spinor-vector η^{aβ} one-forms. Only the bivector one-form B^{ab} is propagating, and carries the same degrees of freedom of the three-form in the usual formulation, its curl \Dcal_{[μ} B^{ab}_{ν]} being related to the F_{μνa b} curl of the three-form. The other one-forms are auxiliary, and the transformation rules on all the fields close on the equations of motion of d=11 supergravity.

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Leonardo Castellani. 2006-04-30. Extended Lie derivatives and a new formulation of D=11 supergravity. https://arxiv.org/abs/hep-th/0604213

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