Global embeddings for branes at toric singularities

TL;DR

This paper presents a method to embed local toric singularities, used in string model building, into compact Calabi-Yau manifolds, analyzing the constraints and examples involving D-branes and F-theory.

Contribution

It introduces a systematic approach for embedding local toric singularities into global Calabi-Yau spaces, including detailed examples with D-branes and F-theory uplift.

Findings

Successful embedding of (dP0)^3 singularity in a Calabi-Yau hypersurface

Constraints on local models imposed by global geometry

Generalization to complete intersections and F-theory backgrounds

Abstract

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.