Heterotic-Type IIA Duality and Degenerations of K3 Surfaces

TL;DR

This paper explores the duality between heterotic and type IIA string theories in four dimensions, focusing on how degenerations of K3 surfaces affect the duality and lead to new insights into solitons and transitions between Calabi-Yau manifolds.

Contribution

It identifies how degenerate K3 fibres correspond to heterotic solitons and uses degeneration theory to analyze singular transitions in dual compactifications.

Findings

Degenerate K3 fibres act as solitons in heterotic string theory.

Degenerations induce singular transitions between Calabi-Yau threefolds.

Some type IIA compactifications lack known heterotic duals.

Abstract

We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic--type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.