Abstract
It has been shown that a four dimensional finite and consistent superstring theory [1] can be constructed by combining any 2-dimensional superconformai field theory with a central charge c=9 with a superstring propagating in flat 4-dimensional Minkowski space-time. Each distinct superconformai field theory corresponds to a possible vacuum state of the full string theory. For N=1 supersymmetry to emerge in this vacuum in 4-dimensions, an N=2 worldsheet supersymmetry is necessary [2]. Gepner has provided [3] a procedure for the construction of a heterotic superstring that satisfies the required properties including modular invariance by using the above ingredients.
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