N=2 Heterotic-Type II duality and bundle moduli

TL;DR

This paper uses duality with type II strings to predict the hypermultiplet moduli space metric in heterotic string compactifications on elliptically fibered K3 surfaces, revealing a layered fibration structure consistent with theoretical expectations.

Contribution

It provides the first prediction of the quaternion-K"ahler metric on hypermultiplet moduli space for heterotic K3 compactifications using duality, especially in the large fiber and base limit.

Findings

The metric has a two-stage fibration structure.

The predicted metric aligns with Kaluza-Klein reduction expectations.

Agreement with duality predictions supports the proposed moduli space structure.

Abstract

Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ depend on a choice of hyperk\"ahler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the $(0,2)$ superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-K\"ahler metric on hypermultiplet moduli space when $\mathfrak{S}$ is elliptically fibered, in the limit of a large fiber and even larger base. The result is in general agreement with expectations from Kaluza-Klein reduction, in particular the metric has a two-stage fibration structure, where the $B$-field moduli are fibered over bundle and metric moduli, while bundle moduli are themselves fibered over metric moduli. A more precise match must await a detailed analysis of $R^2$-corrected ten-dimensional supergravity.