D-Branes on Vanishing del Pezzo Surfaces

Abstract

In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactifi-cation. By means of toric geometry, we classify all the Calabi-Yau manifolds with 3 < h 1,1 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kähler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kähler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima. We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.

Crystal melting and black holes

“…Each strong foundation for a helix defines a physical collection of fractional branes on X which base the quiver [6,7]. The upper triangular matrix S ij = χ (E j , E i ) with ones on the diagonal determines the adjacency of bifundamentals in the quiver gauge theory.…”

“…Although there are many crepant 7 resolutions of the orbifold C 3 /Γ which are all related by flops, there is one distinguished choice such that the tautological sheaves of the resolution are given by a collection of line bundles which are generated by 7 A crepant resolution of a singular Calabi-Yau X is a smooth resolution Y such that c 1 (Y ) = 0.…”

Stability conditions and branes at singularities

“…In other words, the different quivers corresponding to different exceptional collections correspond to different open regions in a generalized Kähler moduli space of our theory. Furthermore, quivers related by mutation can arise by passing to adjacent regions in this moduli space, a procedure related to Seiberg duality [3,4,17]. Without further understanding the relation between Bridgeland's space of stability conditions and the physical moduli space, however, we cannot say if all these regions occur in the actual string theory.…”

“…The use of the topological B-model to explore the gauge theories living on D-branes at singularities has been extremely fruitful in recent years [1,2,3,4,5,6,7,8]. The fundamental feature of this technique is an equivalence of categories between the derived category of coherent sheaves on the resolved singularity and the derived category of representations of the algebra described by the quiver in the dual gauge theory.…”

“…By solving the PicardFuchs equations, one can then determine how the gradings behave as we move around in moduli space. This has been accomplished in many examples [4,11] but can be difficult in general.…”