Note on N=0 string as N=1 string

TL;DR

The paper constructs an explicit similarity transformation linking N=1 and N=0 string theories, demonstrating their spectra are related through a tensor product with a topological sector, thus simplifying the understanding of their equivalence.

Contribution

It provides a concrete similarity transformation that relates N=1 and N=0 string theories, preserving operator algebra and clarifying their spectral relationship.

Findings

The N=1 BRST operator decomposes into N=0 and topological parts.

The physical spectrum of N=1 vacua is isomorphic to N=0 spectrum tensor topological vacuum.

The transformation preserves the operator algebra.

Abstract

A similarity transformation, which brings a particular class of the $N=1$ string to the $N=0$ one, is explicitly constructed. It enables us to give a simple proof for the argument recently proposed by Berkovits and Vafa. The $N=1$ BRST operator is turned into the direct sum of the corresponding $N=0$ BRST operator and that for an additional topological sector. As a result, the physical spectrum of these $N=1$ vacua is shown to be isomorphic to the tensor product of the $N=0$ spectrum and the topological sector which consists of only the vacuum. This transformation manifestly keeps the operator algebra.