A Universal w String Theory

TL;DR

This paper explores a hierarchy of string theories based on $w_N$ algebras, proposing that the $w_{ }$ string theories are special cases of more universal $w_{ }$ and $w_{ abla}$ string frameworks, unifying various models.

Contribution

It introduces a sequence of $w_N$ string theories and conjectures their relation to a more universal $w_{ abla}$ string, unifying different algebraic string models.

Findings

$w_N$ string theories form a sequential embedding structure.

$w_{ abla}$ string theory is proposed as a universal framework.

Specific realizations of $w_N$ strings as special cases of more general theories.

Abstract

It has been shown that there is a sequential embedding structure in a $w_N$\ string theory based on a linearized $W_N$\ algebra. The $w_N$\ string theory is obtained as a special realization of the $w_{N+1}$\ string. The $w_{\infty}$\ string theory is a universal string theory in this sense. We have also shown that there is a similar sequence for $N=1$\ string theory. The $N=1\ w_N$\ string can be given as a special case of the $N=1\ w_{N+1}$\ string. In addition, we show that the $w_3$\ string theory is obtained as a special realization of the $N=1\ w_3$\ string. We conjecture that the $w_N$\ string can be obtained as a special $N=1\ w_N$\ string for general $w_N$. If this is the case, $N=1\ w_{\infty}$\ string theory is more universal since it includes both $N=0$\ and $N=1$\ $w_N$\ string theories.