A Universal w String Theory

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 $N=1w_N$\ string can be given as a special case of the $N=1w_{N+1}$\ string. In addition, we show that the $w_3$\ string theory is obtained as a special realization of the $N=1w_3$\ string. We conjecture that the $w_N$\ string can be obtained as a special $N=1w_N$\ string for general $w_N$. If this is the case, $N=1w_{\infty }$\ string theory is more universal since it includes both $N=0$\ and $N=1$\ $w_N$\ string theories.

19 pages, uses PHYZZX, typological errors corrected, OU-HET 187