World volume Supermembrane Instantons in the light-cone frame

TL;DR

This paper reviews the octonionic duality in supermembranes, deriving self-duality equations, exploring their integrability in specific dimensions, and presenting classical solutions that preserve certain supersymmetries.

Contribution

It introduces the octonionic duality framework for membranes and derives new self-duality equations with solutions in Euclidean space.

Findings

Self-duality equations for supermembranes are derived.

Integrability of the system is analyzed in 7 and 3 dimensions.

Classical Euclidean solutions preserving supersymmetry are presented.

Abstract

In this review we present the octonionic duality for membranes. We start with a discussion on the relation of the Yang Mills theories and the supermembrane Hamiltonian in the light-cone gauge. We further derive the self-duality equations for the membranes and discuss the integrability of the system in 7 and 3 dimensions. Finally, we present classical Euclidean time solutions of these equations and examine the supersymmetries left intact by the self-duality equations.