Lie derivatives along antisymmetric tensors, and the M-theory superalgebra

Leonardo Castellani

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arXiv · hep-th/0508213

Lie derivatives along antisymmetric tensors, and the M-theory superalgebra

Leonardo Castellani

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Abstract

Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials. An extended Lie derivative along antisymmetric tensor fields can be defined, and used to recover a Lie algebra dual to the FDA, that encodes all the symmetries of the theory including those gauged by the p-forms. The general method is applied to the FDA of D=11 supergravity: the resulting dual Lie superalgebra contains the M-theory supersymmetry anticommutators in presence of 2-branes.

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Leonardo Castellani. 2005-08-31. Lie derivatives along antisymmetric tensors, and the M-theory superalgebra. https://arxiv.org/abs/hep-th/0508213

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