Divergences in the Moduli Space Integral and Accumulating Handles in the Infinite-Genus Limit

The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations on the parameters of the uniformizing Schottky group. The growth of the lower bound for the regularized partition function is derived through integration over a subset of the fundamental region.Comment: 26 pages, DAMTP-R/94/1

Configurations of Handles and the Classification of Divergences in the String Partition Function

The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced to geometrical characteristics of the string worldsheet. Some categories of divergences may be eliminated in string theories formulated on compact manifolds.Comment: 24 pages, DAMTP-R/94/1