Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Abstract

We establish a new weak coupling limit in F-theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter $t$ such that computations in the local model become exact as $t \to 0$. More generally, we advocate a modular approach where compact Calabi-Yau geometries are obtained by gluing together local pieces (log Calabi-Yau spaces) into a normal crossing variety and smoothing, in analogy with a similar cutting and gluing approach to topological field theories. We further argue for a holographic relation between F-theory on a degenerate Calabi-Yau and a dual theory on its boundary, which fits nicely with the gluing construction.

Figures (2)

• Figure 1: Gluing a Calabi-Yau manifold from local pieces.
• Figure 2: (A): Global model with $I_5$ singular fibers along a divisor $S$, corresponding to an $SU(5)_{GUT}$ gauge theory. (B): Degenerate version of the global model, in which the singular elliptic fibers describing the $SU(5)_{GUT}$ gauge theory have been pushed to a local $dP_9$-fibration.