Physics of Infinite Complex Structure Limits in eight Dimensions

Abstract

We investigate infinite distance limits in the complex structure moduli space of F-theory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is nevertheless non-trivial enough to improve our understanding of the physics for these limiting geometries, including phenomena of emergence. It also provides a perspective on infinite distance limits from the viewpoint of open strings. The paper has two quite independent themes. In the main part we show that all degenerations of elliptic K3 surfaces at infinite distance as analysed in a companion paper can be interpreted as (partial) decompactification or emergent string limits in F-theory, in agreement with the Emergent String Conjecture. We present a unified geometric picture of the possible towers of states that can become light and illustrate our general claims via the connection between Kulikov models of degenerating K3 surfaces and the dual heterotic string. As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. In the second part we discuss the infinite distance behaviour of certain exact quartic gauge couplings. We encounter a tension with the hypothesis that effective couplings should be fully generated by integrating out massive states. We show that by appropriately renormalizing the string coupling, at least partial emergence can be achieved.

57 pages, 11 figures

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Cited by in corpus (13)

• The Weak Gravity Conjecture: A Review
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Membrane Limits in Quantum Gravity
• Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape
• New Supersymmetric String Moduli Spaces from Frozen Singularities
• Emergent Strings in Type IIB Calabi--Yau Compactifications
• Affine Algebras at Infinite Distance Limits in the Heterotic String
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories