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

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

2005-08-29

arxiv.org/abs/hep-th/0508213v2

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX. Added a missing commutator in the dual Lie algebra of Section 3.2

Scientific paper

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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