Heterotic-Type II duality in the hypermultiplet sector

TL;DR

This paper explores the duality between heterotic string theory on K3 x T^2 and type IIA on Calabi-Yau threefolds, deriving explicit mappings and conjecturing conditions for mirror symmetry in the hypermultiplet sector.

Contribution

It provides an explicit classical map between the moduli spaces and proposes that both Calabi-Yau and its mirror should be K3 fibrations for duality to hold.

Findings

Derived the heterotic hypermultiplet metric for 24 point-like instantons.

Conjectured that X and its mirror are K3 fibrations for duality.

Confirmed results using heterotic/M-theory duality.

Abstract

We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective moduli spaces at the level of the classical effective actions. We determine the parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal form. From the expression of the holomorphic prepotential we are led to conjecture that both X and its mirror must be K3 fibrations in order for the type IIA theory to have an heterotic dual. We then focus on the region of the moduli space where the metric is expressed in terms of a prepotential on both sides of the duality. Applying the duality we derive the heterotic hypermultiplet metric for a gauge bundle which is reduced to 24 point-like instantons. This result is confirmed by using the duality between the heterotic theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on the moduli space of an SU(2) bundle on K3.