New Orientifold Weak Coupling Limits in F-theory

Abstract

We present new explicit constructions of weak coupling limits of F-theory generalizing Sen's construction to elliptic fibrations which are not necessary given in a Weierstrass form. These new constructions allow for an elegant derivation of several brane configurations that do not occur within the original framework of Sen's limit, or which would require complicated geometric tuning or break supersymmetry. Our approach is streamlined by first deriving a simple geometric interpretation of Sen's weak coupling limit. This leads to a natural way of organizing all such limits in terms of transitions from semistable to unstable singular fibers. These constructions provide a new playground for model builders as they enlarge the number of supersymmetric configurations that can be constructed in F-theory. We present several explicit examples for E8, E7 and E6 elliptic fibrations.

45 pages, typos corrected

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• Small resolutions of SU(5)-models in F-theory
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• Theories of Class F and Anomalies
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• Euler Characteristics of Crepant Resolutions of Weierstrass Models
• Mordell-Weil Torsion, Anomalies, and Phase Transitions
• Abelian Gauge Fluxes and Local Models in F-Theory
• The Geometry of SO(3), SO(5), and SO(6) models
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• A new CY elliptic fibration and tadpole cancellation
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Characteristic numbers of elliptic fibrations with non-trivial Mordell-Weil groups
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• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
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• A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• On tadpole relations via Verdier specialization
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• Orientifold limits of singular $F$-theory vacua