D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Mboyo Esole, James Fullwood, Shing-Tung Yau

A D5 elliptic fibration is a fibration whose generic fiber is
modeled by the complete intersection of two quadric surfaces in
P3. They provide simple examples of elliptic fibrations admitting a
rich spectrum of singular fibers (not all on the list of Kodaira)
without introducing singularities in the total space of the fibration
and therefore avoiding a discussion of their resolutions. We study
systematically the fiber geometry of such fibrations using Segre
symbols and compute several topological invariants.

We present for the first time Sen's (orientifold) limits for D5 elliptic fibrations. These orientifold limits describe different weak coupling limits of F-theory to type IIB string theory giving a system of three brane-image-brane pairs in presence of a Z2 orientifold. The orientifold theory is mathematically described by the double cover the base of the elliptic fibration. Such orientifold theories are characterized by a transition from a semi-stable singular fiber to an unstable one. In this paper, we describe the first example of a weak coupling limit in F-theory characterized by a transition to a non-Kodaira (and non-ADE) fiber. Inspired by string dualities, we obtain non-trivial topological relations connecting the elliptic fibration and the different loci that appear in its weak coupling limit. Mathematically, these are very surprising relations relating the total Chern class of the D5 elliptic fibration and those of different loci that naturally appear in the weak coupling limit. We work in arbitrary dimension and are result don't assume the Calabi-Yau condition.