Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-12-09
Int.J.Mod.Phys. A20 (2005) 821-850
Physics
High Energy Physics
High Energy Physics - Theory
TeX, 33 pages
Scientific paper
10.1142/S0217751X05021245
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 $2^{\mit N}$. The product of the coefficient 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 the characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.
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