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.
Highlights
This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. We identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory
The duality between heterotic string theory and Type II string theories hints at non-trivial relations between seemingly totally unrelated mathematical objects
Heterotic string compactifications involve gauge field moduli, whereas only the compactification geometry must be specified for Type II compactifications
Summary
The duality between heterotic string theory and Type II string theories hints at non-trivial relations between seemingly totally unrelated mathematical objects. Starting with the heterotic-type IIA duality in six dimensions, the key principle in understanding the correspondence of discrete data is the idea of adiabatically fibering the dual six dimensional theories over a base P1 [4,5,6]. Armed with this principle, the problem of discrete data correspondence roughly splits into two fronts. We refer to [9] for definitions and explanations concerning the methods of toric geometry used in this article
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