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

Abstract

A D 5 elliptic fibration is a fibration whose generic fiber is modeled by the complete intersection of two quadric surfaces in P 3 . 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 D 5 elliptic fibrations. These orientifolds limit 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 Z 2 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 D 5 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.

M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies

“…This agrees with a formula proved in [33,34]. For similar techniques on computing the Euler characteristics, see [29,50,[57][58][59][60][61].…”

Singularities and gauge theory phases, II

“…For recent works on elliptic Calabi-Yau threefolds see [Cat, DKW, JT, Cat]. Many interesting questions on elliptic fibrations can also be discussed using different starting points than a Weierstrass model [BKMT,AE2,EFY,MP] or considering the weak coupling limit [Sen,CDE,CDW,AE1,AE2,ES].…”

Three-family particle physics models from global F-theory compactifications

“…The second is more concerned with the construction of genus-one or elliptic fibers C which naturally allow for certain generic features of the compactification. In this direction, there have been two major conceptual extensions: One is related to the construction of elliptic curves exhibiting an ever growing number of rational points [13][14][15][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. These permit the construction of elliptically fibered CY-manifolds with a certain number of rational sections and hence, a non trivial Mordell-Weil (MW) group of rational sections.…”