Some Algebraic Aspects of Half-BPS Bound States in M-Theory

TL;DR

This paper explores the algebraic structure of half-BPS bound states in M-theory, revealing how non-marginal solutions relate to marginal ones through E10/K(E10) symmetries and subalgebras.

Contribution

It introduces a novel algebraic framework for describing non-marginal BPS solutions in M-theory using E10/K(E10) and subalgebras, extending previous marginal solution results.

Findings

Non-marginal BPS solutions are exact solutions of the brane sigma-model E10/K(E10).

Non-marginal solutions can be generated from marginal ones via K(E10) transformations.

An elegant algebraic structure underlies the bound states, identified through subalgebras embedded in E10.

Abstract

We revisit non-marginal half-BPS solutions of M-theory in the framework of the possible existence of an underlying E11 Kac-Moody symmetry. In this context, non-marginal BPS solutions of M-theory can be described as exact solutions of the brane sigma-model E10/K(E10), extending results obtained earlier for marginal BPS solutions. We uncover an elegant and simple algebraic structure underlying the bound states by looking at subalgebras embedded in E10. Furthermore, we show that the non-marginal BPS solutions can be obtained from the elementary marginal ones by the action of K(E10) transformations.