On N=1 Superconformal Algebra in the Non-Critical Bosonic String Theory

TL;DR

This paper explores the embedding of non-critical bosonic strings into N=1 fermionic strings, proposing new constructions that suggest non-trivial embeddings and analyzing their BRST charge structures.

Contribution

It introduces two novel constructions for embedding non-critical bosonic strings into N=1 fermionic strings, challenging the notion of triviality in such embeddings.

Findings

Superpartners of physical states are non-physical, indicating no supersymmetry in physical spectrum.

Proposed embeddings are non-trivial and involve specific BRST charge decompositions.

The embeddings include the non-critical NSR string as a special case.

Abstract

In a recent work it has been shown that the bosonic strings could be embedded into a special class of $N=1$ fermionic strings. We argue that the superpartners of any physical state in the spectrum of this fermionic string is non-physical. So, there is no supersymmetry in the space of physical states and the embedding is, in this sense, ``trivial''. We here propose two different constructions as possible candidates of non-trivial embeddings of the non-critical bosonic strings into some special class of $N=1$ fermionic strings of which one is the non-critical NSR string. The BRST charge of the $N=1$ fermionic strings in both cases decompose as $Q_{N=1} = Q_B + {\tilde Q}$, where $Q_B$ is the BRST charge of the bosonic string.