On the equivalence of fermionic string to bosonic string in two dimensions

TL;DR

This paper demonstrates that two-dimensional fermionic string theory is structurally equivalent to a topological model composed of two ghost systems, one of which corresponds to the $c=1$ bosonic string, revealing a deep connection between these theories.

Contribution

It establishes a topological model structure for 2D fermionic string theory and shows its isomorphism to a tensor product involving $c=1$ bosonic string theory, providing new insights into their relationship.

Findings

Fermionic string theory has a topological structure isomorphic to two ghost systems.

One ghost system corresponds to $c=1$ bosonic string theory, the other is trivial.

Discrete states of $c=1$ string are mapped to those of fermionic string theory.

Abstract

Two-dimensional fermionic string theory is shown to have a structure of topological model, which is isomorphic to a tensor product of two topological ghost systems independent of each other. One of them is identified with $c=1$ bosonic string theory while the other has trivial physical contents. This fact enables us to regard two-dimensional fermionic string theory as an embedding of $c=1$ bosonic string theory in the moduli space of fermionic string theories. Upon this embedding, the discrete states of $c=1$ string theory are mapped to those of fermionic string theory, which is considered to be the origin of the similarity between the physical spectra of these two theories. We also discuss a novel BRST operator associated with this topological structure.