On the Uniqueness of String Theory
Nathan Berkovits, Cumrun Vafa · 1993
We show that bosonic strings may be viewed as a particular class of vacua for N = 1 superstrings, and N = 1 superstrings may be viewed as a particular class of vacua for N = 2 strings. Continuing this line of string hierarchies, we are led to search for a universal string theory which includes all the rest as a special vacuum selection. 10/93 One of the most beautiful aspects of string theory is that it has almost no adjustable parameters. The main choice to be made is the selection of a string vacuum. The only nonunique feature seems to be the selection of which worldsheet symmetries we are gauging. If we take the worldsheet gravity theory to be pure gravity (N=0), we get the bosonic strings, for N = 1 supergravity we get the fermionic string, and for N = 2 supergravity we get the N = 2 strings. For closed strings, we can also choose heterotic combinations (p, q) depending on which symmetries we choose for the left- or right-moving degrees of freedom (the most well known example being the (0,1) heterotic string). In this paper we show that the choice of which string we consider may also be viewed just as another choice of string vacuum. In particular we will show that any string vacuum for a (p, q) string can be viewed as a special choice of the string vacuum for (p′, q ′) string with 0 ≤ p ≤ p ′ ≤ 2