An E9 multiplet of BPS states

TL;DR

This paper constructs an infinite multiplet of BPS states in 11D supergravity using E9 symmetry, revealing new solutions and dualities that extend beyond traditional supergravity frameworks.

Contribution

It introduces a novel method combining Weyl reflections and transformations to generate a vast array of BPS solutions related by E9 dualities, including solutions beyond standard 11D supergravity.

Findings

Constructed an infinite E9 multiplet of BPS states.

Revealed new solutions via Weyl transformations and dualities.

Linked E9 dualities to the Geroch group and extended duality concepts.

Abstract

We construct an infinite E9 multiplet of BPS states for 11D supergravity. For each positive real root of E9 we obtain a BPS solution of 11D supergravity, or of its exotic counterparts, depending on two non-compact transverse space variables. All these solutions are related by U-dualities realised via E9 Weyl transformations in the regular embedding of E9 in E10, E10 in E11. In this way we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5 brane and the KK6-monopole, as well as other solutions admitting eight longitudinal space dimensions. A novel technique of combining Weyl reflexions with compensating transformations allows the construction of many new BPS solutions, each of which can be mapped to a solution of a dual effective action of gravity coupled to a certain higher rank tensor field. For real roots of E10 which are not roots of E9, we obtain additional BPS solutions transcending 11D supergravity (as exemplified by the lowest level solution corresponding to the M9 brane). The relation between the dual formulation and the one in terms of the original 11D supergravity fields has significance beyond the realm of BPS solutions. We establish the link with the Geroch group of general relativity, and explain how the E9 duality transformations generalize the standard Hodge dualities to an infinite set of `non-closing dualities'.