The Octonionic Membrane

TL;DR

This paper extends supermembrane solutions in eleven-dimensional supergravity by exploring self-dual and anti-self-dual 4-form configurations in eight transverse dimensions, revealing new solutions with distinct properties and no preserved supersymmetry.

Contribution

It introduces two novel supergravity solutions involving octonionic structures, analyzing their properties and supersymmetry conditions, expanding the understanding of membrane configurations.

Findings

Anti-self-dual solution is asymptotically flat with finite mass.

Both solutions involve octonionic constants but are unrelated to octonionic instantons.

Neither solution preserves supersymmetry.

Abstract

We generalize the supermembrane solution of D=11 supergravity by permitting the 4-form $G$ to be either self-dual or anti-self-dual in the eight dimensions transverse to the membrane. After analyzing the supergravity field equations directly, and also discussing necessary conditions for unbroken supersymmetry, we focus on two specific, related solutions. The self-dual solution is not asymptotically flat. The anti-self-dual solution is asymptotically flat, has finite mass per unit area and saturates the same mass=charge Bogomolnyi bound as the usual supermembrane. Nevertheless, neither solution preserves any supersymmetry. Both solutions involve the octonionic structure constants but, perhaps surprisingly, they are unrelated to the octonionic instanton 2-form $F$, for which $TrF \wedge F$ is neither self-dual nor anti-self-dual.