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

TL;DR

This paper develops an extended Lie derivative framework for antisymmetric tensors in free differential algebras, revealing a dual Lie superalgebra that encodes M-theory supersymmetry, including brane effects.

Contribution

It introduces a novel extended Lie derivative approach for antisymmetric tensors in FDA's, connecting them to a dual Lie superalgebra that captures M-theory symmetries.

Findings

Derived a dual Lie superalgebra for D=11 supergravity

Revealed the M-theory supersymmetry structure with brane contributions

Unified gauge symmetries of antisymmetric tensors in a new algebraic framework

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.