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We construct a cut-off version of nonpertubative closed Bosonic string fieldtheory in the light-cone gauge with imaginary string coupling constant. We showthat the partition function is a continuous function of the string couplingconstant, and conjecture a relation between the formal power series expansionof this partition function and Riemann Surfaces.

Measures on Banach Manifolds, Random Surfaces, and Nonperturbative String Field Theory with Cut-offs