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

TL;DR

This paper investigates the symmetries of the closed bosonic string partition function, analyzing the integration region in Teichmuller space and deriving bounds on the partition function's growth in the infinite-genus limit.

Contribution

It provides a new analysis of the fundamental region in Teichmuller space and relates it to Schottky group parameters, advancing understanding of string theory in complex moduli spaces.

Findings

Derived conditions on the period matrix for the fundamental region

Established growth bounds for the regularized partition function

Connected symmetries with Schottky group parameters

Abstract

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.