Tate Form and Weak Coupling Limits in F-theory

TL;DR

This paper investigates the weak coupling limits of F-theory with non-Abelian gauge groups, classifies resulting singularities, and proposes a new limit that resolves certain conifold singularities incompatible with orientifold symmetry.

Contribution

It introduces a novel weak coupling regime that allows crepant resolutions compatible with orientifold involutions, addressing issues in traditional Tate-based limits.

Findings

Identification of singularity types in weak coupling limits

Resolution of conifold singularities incompatible with orientifold symmetry

Discovery of multiple non-equivalent weak coupling flows affecting gauge groups

Abstract

We consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups.