Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity

TL;DR

This paper introduces a level concept for Lorentzian Kac-Moody algebras and analyzes the representation content of very extended $A_{D-3}$ and $E_8$ at low levels, supporting conjectured symmetries in gravity and supergravity.

Contribution

It defines a new level framework for Lorentzian Kac-Moody algebras and computes their low-level representations, providing evidence for conjectured symmetries in gravity theories.

Findings

Representation content matches conjectured symmetries.

Supports the validity of very extended $A_8$ and $E_{11}$ symmetries.

Provides a new method to analyze algebraic structures in theoretical physics.

Abstract

We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{D-3}$ and $E_8$ (i.e. $E_{11}$) at low levels in terms of $A_{D-1}$ and $A_{10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{11}$ 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.