Note on W3 Realizations of the Bosonic String

TL;DR

This paper explores various realizations of the bosonic string within different $W$-string backgrounds to understand their relation as vacua of a universal string theory.

Contribution

It introduces and analyzes multiple $W$-string realizations of the bosonic string, expanding the understanding of string vacua and their interrelations.

Findings

Different $W$-string backgrounds can realize the bosonic string.

Linearized and non-critical $W$-string realizations are discussed.

Connections between various $W$-string formulations are established.

Abstract

In order to investigate to what extent string theories are different vacua of a general string theory (the ``universal string"), we discuss realizations of the bosonic string as particular background of certain types of $W$-strings. Our discussions include linearized $W_3^{lin}$, non-critical $W_3$, linearized $W_3^{(2)lin}$ and critical $W_3^{(2)}$ realizations of the bosonic string.