Physics of Infinite Complex Structure Limits in eight Dimensions

TL;DR

This paper explores infinite distance limits in the complex structure moduli space of F-theory on K3 surfaces in eight dimensions, providing insights into emergent phenomena, geometric classifications, and gauge coupling behaviors.

Contribution

It offers a unified geometric interpretation of degenerations as decompactification or emergent string limits, and classifies possible gauge algebra extensions in these limits.

Findings

Degenerations correspond to decompactification or emergent strings.

Classified maximal non-abelian Lie algebras in limits.

Partial emergence observed after renormalizing string coupling.

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.