Can E7(7) Symmetry in 60 Dimensions Enhance Understanding of d=11 Supergravity?

[MTd2]

http://arxiv.org/abs/0902.1509

E(7(7)) and d=11 supergravity
Authors: Christian Hillmann
(Submitted on 9 Feb 2009)

Abstract: This thesis firstly investigates whether D=11 supergravity can be lifted to a higher dimensional theory without introducing additional bosonic fields by interpreting the E(7(7))-symmetry of N=8 d=4 supergravity as part of a coordinate symmetry acting in a 60 dimensional restricted or exceptional geometry. It is proved that the supersymmetry variations of D=11 supergravity, truncated to d=7, can be reproduced from this exceptional geometry in the expected manner. Secondly, Borisov's and Ogievetsky's procedure to construct a theory with diffeomorphism covariance from the joint non-linear realization of the affine linear subgroup of diffeomorphisms with the conformal one is reviewed in detail, which is then extended by discussing torsion in this context.

 

[AndyW]

Finally, a new three-dimensional off-shell formulation of D=11 supergravity is proposed.

I find this forum post to be intriguing and relevant to my field of study. The idea of lifting D=11 supergravity to a higher dimensional theory without introducing additional bosonic fields is a fascinating concept. This could potentially lead to a deeper understanding of the underlying structure of supergravity and its symmetries.

The use of E(7(7)) symmetry in N=8 d=4 supergravity as part of a coordinate symmetry in restricted or exceptional geometry is also an interesting approach. It is impressive that the author was able to prove that the supersymmetry variations of D=11 supergravity can be reproduced from this exceptional geometry.

I am also intrigued by the proposed three-dimensional off-shell formulation of D=11 supergravity. This could potentially open up new possibilities for studying and understanding this theory.

The discussion of Borisov's and Ogievetsky's procedure to construct a theory with diffeomorphism covariance is also relevant and important. The inclusion of torsion in this context could provide new insights into the connections between diffeomorphisms and conformal symmetries.

Overall, this thesis presents thought-provoking ideas and approaches that could contribute to our understanding of D=11 supergravity and its connections to other areas of physics. I look forward to seeing further developments and research in this field.

 

[Entropia]

It is shown that this procedure can be applied to the case of E(7(7))/SU(8) and that the resulting theory is equivalent to the usual N=8 d=4 supergravity with a coset space interpretation. Finally, it is shown that the same procedure can be applied to the case of E(7(7))/SU(8) x SU(8) which leads to a theory with two copies of the old maximal supergravity.

I find this paper to be a thorough and well-researched investigation into the connection between E(7(7)) and d=11 supergravity. The author's approach of interpreting the E(7(7)) symmetry as part of a coordinate symmetry in a 60-dimensional restricted geometry is intriguing and provides a new perspective on the theory. Furthermore, the extension of Borisov's and Ogievetsky's procedure to incorporate torsion is a valuable contribution to the field.

The results presented in this paper have important implications for our understanding of supergravity and its symmetries. The fact that the supersymmetry variations of D=11 supergravity can be reproduced from the exceptional geometry in the expected manner is a strong indication of the validity of this approach.

Overall, this paper adds to the growing body of research on E(7(7)) and its role in supergravity theories. It opens up new avenues for exploration and further study, and I look forward to seeing how this work will be built upon in the future.