Open Access
March 2011 Extended Lie Derivatives and a New Formulation of $D=11$ Supergravity
Leonardo Castellani
J. Phys. Math. 3: 1-4 (March 2011). DOI: 10.4303/jpm/P110505


Introducing an extended Lie derivative along the dual of $A$, the $3$-form field of $D=11$ supergravity, the full diffeomorphism algebra of $D=11$ supergravity is presented. This algebra suggests a new formulation of the theory, where the $3$-form field $A$ is replaced by bivector $B^{ab}$, bispinor $B^{\alpha\beta}$, and spinor-vector $\eta^{a\beta}$ $1$-forms. Only the bivector $1$-form $B^{ab}$ is propagating, and carries the same degrees of freedom of the $3$-form in the usual formulation, its curl $\mathcal{D}_{[\mu} B^{ab}_{\nu]}$ being related to the $F_{\mu \nu a b}$ curl of the $3$-form. The other $1$-forms are auxiliary, and the transformation rules on all the fields close on the equations of motion of $D=11$ supergravity.


Download Citation

Leonardo Castellani. "Extended Lie Derivatives and a New Formulation of $D=11$ Supergravity." J. Phys. Math. 3 1 - 4, March 2011.


Published: March 2011
First available in Project Euclid: 29 January 2013

zbMATH: 1264.83042
Digital Object Identifier: 10.4303/jpm/P110505

Primary: 53Z05 , 83F50

Keywords: cosmology , Differential geometry , Relativity and gravitational theory

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
Back to Top