D=11 Supermembrane Instantons, W(infty) Strings and the Super Toda Molecule

TL;DR

This paper constructs exact instanton solutions for D=11 supermembranes using super Yang-Mills theories with infinite-dimensional symmetry, revealing connections to super W-infinity strings and the super Toda molecule, with implications for quantum consistency.

Contribution

It introduces a novel approach to supermembrane instantons via super Yang-Mills theories based on SU(∞), linking super Toda molecules to super W-infinity strings and exploring their quantum properties.

Findings

Exact instanton solutions for D=11 supermembranes are constructed.

Super Toda molecule equations are derived from super Yang-Mills theories.

Connections between supermembranes, super W-infinity strings, and integrability are discussed.

Abstract

Exact instanton solutions to $D=11$ spherical supermembranes moving in flat target spacetime backgrounds are construted. Our starting point is Super Yang-Mills theories, based on the infinite dimensional $SU(\infty)$ group, dimensionally reduced to one time dimension. In this fashion the super-Toda molecule equation is recovered preserving only one supersymmetry out of the $N=16$ that one would have obtained otherwise. It is conjectured that the expected critical target spacetime dimensions for the (super) membrane, ($D=11$) $D=27$ is closely related to that of the $noncritical$ (super) $W_{\infty}$ strings. A BRST analysis of these symmetries should yield information about the quantum consistency of the ($D=11$) $D=27$ dimensional (super) membrane. Comments on the role that Skyrmions might play in the two types of Spinning- Membrane actions construted so far is presented at the conclusion. Finally, the importance that integrability on light-lines in complex superspaces has in other types of solutions is emphasized.