Global embeddings for branes at toric singularities

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.

Deformations, moduli stabilisation and gauge couplings at one-loop

“…This phenomenon was also observed [51] for specific deformations of complex co-dimension 2 singularities on the subspace T 4 (i) /Z 2 of the orbifold T 6 /(Z 2 × Z 6 ) with discrete torsion and can be resolved by turning on a correction-term ε (1) 3 depending on the respective deformation parameter, as depicted in the lower diagrams of figures 3 (f) and (g). A similar consideration holds for the fixed points (22) and (44) which are also deformed, but now for a non-vanishing deformation parameter ε (1) 3 = 0. Further details about the counter-terms can be found in appendix B.…”

“…[36], which would offer us the necessary techniques to resolve exceptional two-and four-cycles through blow-ups. Toric singularities and blow-up resolutions of divisor four-cycles happen to be part of the modus operandi for constructing chiral gauge theories on the Type IIB side [37][38][39][40][41][42][43][44][45][46][47] using fractional D3-branes located at the singularities or D7-branes wrapping the resolved fourcycles. However, in the case of Type IIA model building with fractional D6-branes on orbifolds with discrete torsion, the orbifold singularities have to be deformed rather than blown up, which forces us to consider different tools from algebraic geometry: by viewing two-tori as elliptic curves in the weighted projective space P 2 112 , a factorisable toroidal orbifold with discrete torsion can be described as a hypersurface in a weighted projective space, with its topology being a double cover of P 1 × P 1 × P 1 .…”

D-brane instantons on non-Spin cycles

“…As an example, in [20] we show how the O(1) instanton discussed in this paper can be used to stabilize the Kähler moduli in a model introduced in [21].…”

Wavefunctions on magnetized branes in the conifold

“…Though in a different context, the flux configurations on D7-branes in 4D toric variety is discussed in refs. [34][35][36].…”