Abstract
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) (dP 0)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.
Highlights
A convenient bottom-up approach to model building in string theory is to consider Dbranes placed at local geometric singularities in a compactification manifold [1,2,3,4,5,6]
As an illustration of our discussion we focus on D3 and D7-branes on3 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
In this paper we have provided a prescription for how to find global realizations of local models of gauge and matter content in which D-branes are placed at toric singularities
Summary
A convenient bottom-up approach to model building in string theory is to consider Dbranes placed at local geometric singularities in a compactification manifold [1,2,3,4,5,6]. The natural place to look for such global realizations is in terms of Calabi-Yau manifolds given as hypersurfaces in toric varieties. The class of global models that we study can all be described as follows: consider a Calabi-Yau manifold, M , described in terms of a hypersurface constraint in a four dimensional toric variety A∇ obtained from the four dimensional polytope ∇. There may be an embedding into a Calabi-Yau constructed as a complete intersection within a higher dimensional toric variety Since we are mainly interested in gauge theories with U(N ) factors only, we focus on Z2 permutation involutions in which pairs of branes at singularities are exchanged These type IIB compactifications are up-lifted to (singular) Calabi-Yau fourfolds in F-theory.
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