On The Instanton Solutions Of The Self-Dual Membrane In Various Dimensions

TL;DR

This paper develops methods to find explicit solutions for self-dual supermembranes in higher dimensions, focusing on symmetric configurations and the SU(∞) Toda equation, with detailed examples illustrating the approach.

Contribution

It introduces a systematic method for solving self-dual supermembrane equations in 4+1 and 8+1 dimensions, emphasizing axial symmetry and the SU(∞) Toda equation.

Findings

Explicit solutions for self-dual supermembranes are obtained.

The SU(∞) Toda equation is central to symmetric configurations.

Several detailed examples demonstrate the solution methods.

Abstract

We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to play a central role, and a specific method of determining all the periodic solutions are suggested. A number of examples are studied in detail.