Perturbative Prepotential and Monodromies in N=2 Heterotic Superstring

TL;DR

This paper analyzes the one-loop prepotential in N=2 heterotic superstring models, revealing how singularities from massless states alter duality symmetries, which are described by the fundamental group of the moduli space.

Contribution

It provides an exact perturbative description of duality transformations in N=2 heterotic models, linking singularities to the fundamental group of the moduli space.

Findings

Logarithmic singularities occur at specific moduli space surfaces.

Duality symmetry group becomes a representation of the fundamental group.

For two moduli, the fundamental group is a braid group, determining duality transformations.

Abstract

We discuss the prepotential describing the effective field theory of N=2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.