Abstract
We investigate exceptional generalised diffeomorphisms based on E (8(8)) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL(n + 1) is sketched. Some related issues are discussed.
Highlights
More on this in the discussion section
What has been done for E8 above applies in spirit to enhanced symmetries arising on dimensional reduction of gravity from 3 + n to 3 dimensions due to the appearance of a dual gravity field
The dual gravity field does not carry any local degrees of freedom, and it becomes clear that the restricted SL(n + 1) transformations should not be counted as removing any local degrees of freedom beyond the ones removed by the generalised diffeomorphisms
Summary
We will revisit the concepts of covariance and closure, especially how they are linked together, for the cases known to work: ordinary diffeomorphisms, double diffeomorphisms, and exceptional diffeomorphisms for n ≤ 7. Let us first formalise what covariance and closure means The latter is simple, it means that the generators commute to a transformation with some parameter:. Covariance means, on the other hand, that the transformed vector LξV is a vector, when the vectorial transformation of both V and ξ are taken into account. ∆η(LξV M ) = − ZMN T QZT P RS + ZMP RQδSN ∂N ∂P ηRξS V Q If this vanishes, with the help of the section condition, the transformation is covariant, and L = Lfor a torsion-free connection. With the help of the section condition, the transformation is covariant, and L = Lfor a torsion-free connection This can be shown explicitly for all the cases up to n = 7 (eq (2.3) above). We should stress that the reasoning only holds for transformations constructed with naked derivatives
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
