BPS States, String Duality, and Nodal Curves on K3

TL;DR

This paper explores the enumeration of BPS states in Type II string theory on K3 surfaces by connecting supersymmetric cycles to rational curves with double points, revealing a link to the bosonic string partition function.

Contribution

It establishes a novel relationship between BPS state counting, supersymmetric cycles, and rational curves on K3, utilizing the bosonic string partition function.

Findings

Counting of BPS states relates to rational curves with double points on K3.

The generating function matches the left-moving partition function of the bosonic string.

Provides a new geometric interpretation of BPS state enumeration.

Abstract

We describe the counting of BPS states of Type II strings on K3 by relating the supersymmetric cycles of genus $g$ to the number of rational curves with $g$ double points on K3. The generating function for the number of such curves is the left-moving partition function of the bosonic string.