Abstract
It has been shown that there is a sequential embedding structure in a wN string theory based on a linearized WN algebra. The wN string theory is obtained as a special realization of the wN+1 string. The w∞ 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 wN string can be given as a special case of the N = 1 wN+1 string. In addition, we show that the w3 string theory is obtained as a special realization of the N = 1 w3 string. We conjecture that the wN string can be obtained as a special N = 1 wN string for general wN. If this is the case, the N = 1 w∞ string theory is more universal since it includes both N = 0 and N = 1 wN string theories.
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