The IIA, IIB and eleven dimensional theories and their common E_{11} origin
Abstract
Description
We show that the commonly considered half BPS solutions of eleven dimensional supergravity and the ten dimensional type II theories, when expressed in terms of $E_{11}$ group elements, take the universal form $\exp(-{1\over 2}ln N β\cdot H)\exp((1-N)E_β)$. Using this formula we find new potential solutions to the $E_{11}$ non-linearly realisations corresponding to active fields which are beyond those in the supergravity approximations. These include the space filling nine brane of the IIB theory. We use $E_{11}$ to give a correspondence between the fields of the eleven dimensional and the IIA and IIB non-linear realisations without assuming any dimensional reduction. As one consequence, we find the eleven dimensional origin of the eight brane solution of the massive IIA theory.
27 pages, plain tex. typos corrected, one equation and one reference added
27 pages, plain tex. typos corrected, one equation and one reference added