Remarks on E11 approach

TL;DR

This paper explores various aspects of the $E_{11}$ approach to superstring/M-theory, including subgroup structures, algebraic relations, and potential supersymmetry formulations, aiming to deepen understanding of the algebraic framework underlying these theories.

Contribution

It investigates the structure of $E_{11}$ and related subgroups, their connections to brane charges, and proposes possible supersymmetry relations within the $E_{11}$ framework.

Findings

Analysis of $Z_2$ orbifolds of $E_n$ and their relation to Kac-Moody algebras

Identification of a weight in $EE_{11}$ coinciding with the $l_1$ weight containing brane charges

Observation of the potential relevance of coadjoint orbits in $E_{11}$ equations of motion

Abstract

We consider a few topics in $E_{11}$ approach to superstring/M-theory: even subgroups ($Z_2$ orbifolds) of $E_{n}$, n=11,10,9 and their connection to Kac-Moody algebras; $EE_{11}$ subgroup of $E_{11}$ and coincidence of one of its weights with the $l_1$ weight of $E_{11}$, known to contain brane charges; possible form of supersymmetry relation in $E_{11}$; decomposition of $l_1$ w.r.t. the $SO(10,10)$ and its square root at first few levels; particle orbit of $l_1 \ltimes E_{11}$. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in $E_{11}$.