A Search for New (2,2) Strings

TL;DR

This paper explores new string theories in (2,2) dimensions by extending known algebraic structures, discovering an additional string theory beyond the established N=2 and N=1 models, and analyzing its spectrum and interactions.

Contribution

It introduces a previously unknown string theory based on an algebra outside the N=4 superconformal algebra, expanding the landscape of (2,2) string models.

Findings

Discovery of a new (2,2) string theory outside N=4 algebra

Analysis of the spectrum of the new theory

Investigation of the interactions within this new framework

Abstract

There are at present two known string theories in $(2,2)$ dimensions. One of them is the well known $N=2$ string, and the other one is a more recently constructed $N=1$ spacetime supersymmetric string. They are both based on certain twistings and/or truncations of the small $N=4$ superconformal algebra, realised in terms of $(2,2)$ superspace variables. In this paper, we investigate more general possibilities for string theories based on algebras built with the same set of fields. We find that there exists one more string theory, based on an algebra which is not contained within the $N=4$ superconformal algebra. We investigate the spectrum and interactions of this theory.