EFFECTIVELY CLOSED INFINITE-GENUS SURFACES AND THE STRING COUPLING

Abstract

The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category OG, which is characterized by the vanishing capacity of the ideal boundary. The cardinality of the maximal set of end points is shown to be 2N. The product of the coefficient of the genus-g superstring amplitude in four dimensions by 2g in the g→∞ 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 the characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.