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.

Figures (11)

• Figure 1: Degeneration of the elliptic fiber as we take the weak coupling limit $C\rightarrow 0$. This illustrates the case of the limit presented in §\ref{['IntroE71']} and §\ref{['IntroE6Lim']}. The limit $h\rightarrow 0$ is a specialization to the orientifold locus $h=0$. As we take the weak coupling limit ($C\rightarrow 0$), the elliptic curve reduces to the union of two nonsingular rational curves intersecting transversally at two distinct points. Topologically, this is two spheres meeting at two distinct points. If we specialize to $h=0$ as we take $C\rightarrow 0$, the two rational curves become tangent to each other at a point. In order to have a better understanding of the orientifold configuration, we can get to $C=h=0$ by taking a different road. If we first specialize to $h=0$ before taking the weak coupling limit, the elliptic fiber does not denegerate. However, once we take the weak coupling limit $C\rightarrow 0$ after taking $h=0$, all the elliptic fibers flow to $e=f=g=0$ which corresponds to two 2-spheres tangent at a point.
• Figure 2: Singularities of $E_8$ fibrations
• Figure 3: Singularities of $E_7$ fibrations
• Figure 4: Singularities of cubic curves
• Figure 5: Singular fibers of $E_6$ fibrations

Theorems & Definitions (11)

• Remark 1.1
• Proposition 4.1
• Proposition 4.2: Sethi:1996es, Klemm:1996ts
• Theorem 4.3
• Remark 4.4
• proof : Proof of Theorem \ref{['SVWup']}
• Claim 4.5
• Claim 4.6
• Claim 4.7
• Claim 4.8