New F-theory lifts

TL;DR

The paper addresses the challenge of lifting perturbative IIB orientifolds on complete intersection Calabi–Yau threefolds to F-theory by constructing the base as a $\mathbb{Z}_2$ quotient of the CY3 and embedding it into a Weierstrass elliptic fibration inside a toric ambient space, yielding a Calabi–Yau fourfold $Y_4$. The author demonstrates the method explicitly for (i) the quintic with an O3-plane and (ii) a smooth, O3-free $\mathbb{W}\mathbb{CP}^2_{1,1,2,2,2}(8)$ orientifold, using the tachyon condensation picture for D7-branes and a detailed toric construction of the base and elliptic fiber. A key result is that the curvature-induced D3-charge computed from $\chi(Y_4)$, $Q^c=\chi(Y_4)/12$, matches the IIB K-theory prediction in both cases (with the O3 contributing as expected only in the singular case), providing a nontrivial check of the lift. The work broadens F-theory model-building by enabling lifts from general CICYs with arbitrary orientifold involutions and clarifies the role of O3-planes in the F-theory context, with potential implications for instanton-induced superpotentials.

Abstract

In this note, a procedure is developed to explicitly construct non-trivial F-theory lifts of perturbative IIB orientifold models on Calabi-Yau complete intersections in toric varieties. This procedure works on Calabi-Yau orientifolds where the involution coordinate can have arbitrary projective weight, as opposed to the well-known hypersurface cases where it has half the weight of the equation defining the CY threefold. This opens up the possibility of lifting more general setups, such as models that have O3-planes.