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

TL;DR

This paper classifies divergences in the regularized partition function of closed bosonic string theory, linking them to geometric features of the worldsheet and exploring their elimination on compact manifolds.

Contribution

It introduces a new classification scheme for divergences based on handle configurations and their relation to worldsheet geometry.

Findings

Identifies three types of divergences distinguished by genus dependence.

Links divergences to geometrical features of the string worldsheet.

Shows some divergences can be removed on compact manifolds.

Abstract

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.