Fock representations of non-centrally extended super-diffeomorphism algebras

TL;DR

This paper constructs Fock representations for non-central extensions of super-diffeomorphism algebras, revealing that the superconformal algebra's special role in superstring theory is not fundamental.

Contribution

It introduces new Fock representations for extended super-diffeomorphism algebras and challenges the assumed uniqueness of the superconformal algebra in superstring theory.

Findings

Constructed Fock representations acting on superspace trajectories

Derived superconformal algebra as a restriction, showing its non-uniqueness

Challenged the assumption of the superconformal algebra's distinguished role

Abstract

A class of Fock representations of non-central extensions of the super-diffeomorphism algebra in (N+1|M) dimensions is constructed, by superization of the paper [physics/9705040]. The representations act on trajectories in (N|M)-dimensional superspace, the extra dimension being the parameter along the trajectory. The restrictions to various subalgebras are considered. In particular, the centrally extended superconformal algebra is obtained by restriction to the contact superalgebra K(1|1). This shows that one of the basic assumptions in superstring theory (the distinguished nature of the superconformal algebra) is incorrect.