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

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

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