$N\!=\!8$ Superconformal Algebra and the Superstring

TL;DR

This paper explores the $N=8$ superconformal algebra in superstring theory across various dimensions, revealing its connection to super-Poincaré symmetry and discussing its properties and implications.

Contribution

It establishes the relationship between world-sheet superconformal symmetry and target space super-Poincaré symmetry, generalizes this to 10 dimensions, and analyzes the properties of the $N=8$ superconformal algebra.

Findings

Superstring invariance under $N= D-2$ superconformal algebra in multiple dimensions.

Connection between world-sheet symmetry and target space symmetry.

Analysis of the properties and implications of the $N=8$ superconformal algebra.

Abstract

The superstring in $D\!=\!3,4$ and 6 is invariant under an $N\!=\!D\!-\!2$ superconformal algebra based on $\widehat{S^{D-3}}$. There is a direct relationship between this (world-sheet) symmetry and the super-Poincar\'e (target space) symmetry. We establish this relationship using the light-cone gauge, show how the statement generalizes to $D\!=\!10$ and examine the properties of the $N\!=\!8$ superconformal algebra and the possible implications of its existence.