The IIA, IIB and eleven dimensional theories and their common E_{11} origin

TL;DR

This paper demonstrates that key solutions in eleven-dimensional supergravity and type II theories can be expressed universally using $E_{11}$ group elements, leading to new solutions and insights into their interrelations without dimensional reduction.

Contribution

It introduces a universal $E_{11}$-based formula for BPS solutions, revealing new solutions and clarifying the connection between eleven-dimensional and type II theories.

Findings

Derived a universal $E_{11}$ expression for BPS solutions.

Discovered new solutions including the space-filling nine brane.

Established the eleven-dimensional origin of the massive IIA eight brane.

Abstract

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 $\exp(-{1\over 2}ln N \beta\cdot H)\exp((1-N)E_\beta)$. 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.