Tate Form and Weak Coupling Limits in F-theory

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.

34 pages

References in corpus (13)

• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• Lectures on F-theory compactifications and model building
• Les Houches Lectures on Constructing String Vacua
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• D-brane Deconstructions in IIB Orientifolds
• Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
• Higgs Bundles and UV Completion in F-Theory
• F-theory uplifts and GUTs
• New F-theory lifts
• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• A Global SU(5) F-theory model with Wilson line breaking
• GUT theories from Calabi-Yau 4-folds with SO(10) Singularities
• Non-simply-laced Lie algebras via F theory strings

Cited by in corpus (16)

• The fate of U(1)'s at strong coupling in F-theory
• TASI Lectures on F-theory
• Flopping and Slicing: SO(4) and Spin(4)-models
• D(-1)-Instanton Superpotential In String Theory
• The Geometry of the SU(2)$\times$ G${}_2$-model
• The Geometry of SO(3), SO(5), and SO(6) models
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• The Geometry of F${}_4$-Models
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• On the Standard Model Group in F-theory
• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
• Discrete anomalies in supergravity and consistency of string backgrounds
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• On the Sen limit squared
• Orientifold limits of singular $F$-theory vacua