Heterotic-Type IIA Duality and Degenerations of K3 Surfaces

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.

76 pages, 8 figures; v2: minor changes

References in corpus (7)

• New Aspects of Heterotic--F Theory Duality
• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
• The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
• Instantons, Hypermultiplets and the Heterotic String
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• Matter in transition
• Noether-Lefschetz theory and the Yau-Zaslow conjecture

Cited by in corpus (10)

• Tensionless Strings and the Weak Gravity Conjecture
• The Asymptotic Weak Gravity Conjecture in M-theory
• Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• Modular Curves and the Refined Distance Conjecture
• NS5-Branes and Line Bundles in Heterotic/F-Theory Duality
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Direct Computation of Monodromy Matrices and Classification of 4d N=2 Heterotic--IIA Dual Vacua