Physikalische Mathematik

Lie Derivatives along Anti symmetric Tensors, and the M-Theory Super algebra

Abstract

Leonardo Castellani

Free differential algebras (FDAs) provide an algebraic setting for field theories with antisymmetric tensors. The “presentation” of FDAs 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. MSC 2010: 53Z05, 83F50.