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 Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 601

Effectively Closed Infinite-Genus Surfaces and the String Coupling

S.B. Davis

The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality of the maximal set of endpoints is shown to be $2^{\cal N}$. The product of the genus-$g$ superstring amplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is an exponential function of the genus with a base comparable in magnitude to the unified gauge coupling. The value of the string coupling is consistent with characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.

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