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

Abstract

A D5 elliptic fibration is a fibration whose generic fiber is mod- eled 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, thus avoiding a discussion of their resolutions. We study systematically the fiber geometry of such fibrations using Segre symbols and com- pute several topological invariants. We present for the first time Sen’s (orientifold) limits for D5 elliptic fibrations. These orientifolds limits describe different weak coupling limits of F-theory to type IIB string theory giving a sys- tem of three brane-image-brane pairs in presence of a Z2 orien- tifold. The orientifold theory is mathematically described by the double cover the base of the elliptic fibration. Such orientifold the- ories 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 which re- late the total Chern class of the D5 elliptic fibration and those of different loci that naturally appear in the weak coupling limit. We work over bases of arbitrary dimension and our results are inde- pendent of any Calabi-Yau hypothesis.