Heterotic String Corrections from the Dual Type II String

TL;DR

This paper develops a duality-based method to compute alpha'-corrections in heterotic string moduli spaces, revealing new instanton effects and extending geometric engineering techniques to hypermultiplet moduli.

Contribution

It introduces a novel approach using dual type IIA strings to calculate corrections in heterotic compactifications, including instanton effects and hyperkaehler limits.

Findings

Computed alpha'-corrections for heterotic moduli spaces.

Identified mixed worldsheet and spacetime instantons.

Extended geometric engineering to hypermultiplet moduli.

Abstract

We introduce a method of using the a dual type IIA string to compute alpha'-corrections to the moduli space of heterotic string compactifications. In particular we study the hypermultiplet moduli space of a heterotic string on a K3 surface. One application of this machinery shows that type IIB strings compactified on a Calabi-Yau space suffer from worldsheet instantons, spacetime instantons and, in addition, "mixed" instantons which in a sense are both worldsheet and spacetime. As another application we look at the hyperkaehler limit of the moduli space in which the K3 surface becomes an ALE space. This is a variant of the "geometric engineering" method used for vector multiplet moduli space and should be applicable to a wide range of examples. In particular we reproduce Sen and Witten's result for the heterotic string on an A1 singularity and a trivial bundle and generalize this to a collection of E8 point-like instantons on an ALE space.