Aspects of the Hypermultiplet Moduli Space in String Duality

TL;DR

This paper explores the duality between type IIA string theory and heterotic string theory, focusing on the hypermultiplet moduli space and its mathematical structure, revealing deep geometric correspondences and implications for nonperturbative effects.

Contribution

It provides a detailed analysis of the hypermultiplet moduli space in dual string theories, highlighting a novel identification with integral cohomology structures and implications for mirror symmetry.

Findings

Identification of the hypermultiplet moduli space with integral cohomology structures

Insights into nonperturbative effects in both string theories

Examples involving bundles and point-like instantons on K3 surfaces

Abstract

A type IIA string (or F-theory) compactified on a Calabi-Yau threefold is believed to be dual to a heterotic string on a K3 surface times a 2-torus (or on a K3 surface). We consider how the resulting moduli space of hypermultiplets is identified between these two pictures in the case of the E8xE8 heterotic string. As examples we discuss SU(2)-bundles and G2-bundles on the K3 surface and the case of point-like instantons. We are lead to a rather beautiful identification between the integral cohomology of the Calabi-Yau threefold and some integral structures on the heterotic side somewhat reminiscent of mirror symmetry. We discuss the consequences for probing nonperturbative effects in the both the type IIA string and the heterotic string.