Lie derivatives along antisymmetric tensors, and the M-theory superalgebra
Abstract
Description
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.
11 pages, LaTeX. Added a missing commutator in the dual Lie algebra of Section 3.2
11 pages, LaTeX. Added a missing commutator in the dual Lie algebra of Section 3.2