P1-fibrations in F-theory and string dualities

Abstract

© 2022, International Press, Inc.. All rights reserved.In this work, we study F-theory compactifications on elliptically fibered Calabi-Yau n-folds which have P1-fibered base manifolds. Such geometries, which we study in both 4-and 6-dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/F-theory duality. We discuss the most general formulation of P1-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4-and 6-dimensions we find transitions whereby the base of a P1-bundle can change nature, or “jump”, at certain loci in complex structure moduli space. We discuss the implications of this jumping for the associated heterotic duals. We argue that P1-bundles with only rational sections lead to heterotic duals where the Calabi-Yau manifold is elliptically fibered over the section of the P1 bundle, and not its base. As expected, we see that degenerations of the P1 fibration of the F-theory base correspond to 5-branes in the dual heterotic physics, with the exception of cases in which the fiber degenerations exhibit monodromy. Along the way, we discuss a set of useful formulae and tools for describing F-theory compactifications on this class of Calabi-Yau manifolds.