Bracket Symmetries of the Classical N=1 String

TL;DR

This paper extends Moore's analysis to the N=1 superstring, demonstrating that all amplitudes with bosonic and fermionic states can be derived from massless state amplitudes using bracket relations, simplifying calculations.

Contribution

It generalizes Moore's bracket analysis to the N=1 superstring, enabling expression of complex amplitudes solely in terms of massless states and their bracket relations.

Findings

All amplitudes involving bosonic and fermionic states can be expressed via massless amplitudes.

4-point massless amplitudes can be derived using bracket relations and analyticity.

Potential extension to higher point massless amplitudes is suggested.

Abstract

We show that it is possible to extend Moore's analysis of the classical scattering amplitudes of the bosonic string to those of the N=1 superstring. Using the bracket relations we are able to show that all possible amplitudes involving both bosonic and fermionic string states at arbitrary mass levels can be expressed in terms of amplitudes involving only massless states. A slight generalization of Moore's original definition of the bracket also allows us to determine the 4-point massless amplitudes themselves using only the bracket relations and the usual assumptions of analyticity. We suggest that this should be possible for the higher point massless amplitudes as well.