4 research outputs found
Very Extended and at low levels, Gravity and Supergravity
We define a level for a large class of Lorentzian Kac-Moody algebras. Using
this we find the representation content of very extended and
(i.e. ) at low levels in terms of and
representations respectively. The results are consistent with the conjectured
very extended and symmetries of gravity and maximal supergravity
theories given respectively in hep-th/0104081 and hep-th/0107209. We explain
how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference
expanded
E_11 and M Theory
We argue that eleven dimensional supergravity can be described by a
non-linear realisation based on the group E_{11}. This requires a formulation
of eleven dimensional supergravity in which the gravitational degrees of
freedom are described by two fields which are related by duality. We show the
existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde
E11, generalised space-time and equations of motion in four dimensions
We construct the non-linear realisation of the semi-direct product of E11 and
its first fundamental representation at low levels in four dimensions. We
include the fields for gravity, the scalars and the gauge fields as well as the
duals of these fields. The generalised space-time, upon which the fields
depend, consists of the usual coordinates of four dimensional space-time and
Lorentz scalar coordinates which belong to the 56-dimensional representation of
E7. We demand that the equations of motion are first order in derivatives of
the generalised space-time and then show that they are essentially uniquely
determined by the properties of the E11 Kac-Moody algebra and its first
fundamental representation. The two lowest equations correctly describe the
equations of motion of the scalars and the gauge fields once one takes the
fields to depend only on the usual four dimensional space-time
The symmetry of M-theories
We consider the Cartan subalgebra of any very extended algebra Script G+++ where Script G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions Script G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of Script G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory