Genus Two Surface and Quarter BPS Dyons: The Contour Prescription

TL;DR

This paper investigates the role of genus two surfaces in calculating the spectrum of quarter BPS dyons in N=4 string theories, providing a contour prescription for partition function integration across moduli space walls.

Contribution

It introduces a genus two surface framework for dyon spectrum analysis and derives a precise contour prescription for partition function integration.

Findings

Correct contour prescription for spectrum calculation

Representation of dyons as string network configurations

Insights into moduli space wall crossing behavior

Abstract

Following the suggestion of hep-th/0506249 and hep-th/0612011, we represent quarter BPS dyons in N=4 supersymmetric string theories as string network configuration and explore the role of genus two surfaces in determining the spectrum of such dyons. Our analysis leads to the correct contour prescription for integrating the partition function to determine the spectrum in different domains of the moduli space separated by the walls of marginal stability.