$E_8$ geometry
arXiv:1504.04843
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.
plain tex, 24 pp.; v2: refs. added, a sign misprint corrected (eq. 2.7); v3: minor changes, refs. added