Abstract
An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in detail. The possibilities for the ‘‘geometric’’ and ISS mechanisms of dynamical SUSY breaking are discussed. As an example, we construct the ISS vacuum for the del Pezzo 6 singularity.
Highlights
The construction is analytic, that is, the CY manifolds are described by a system of equations in the È1 bundles over the projective spaces. We argue that this construction can be used for the geometrical SUSY breaking 8 as well as for the compactification of ISS 10
We find a compact CY manifold with del Pezzo 6 singularity and some conifolds such that some 2-cycles on del Pezzo are homologous to the 2-cycles on the conifolds, that is, this manifold can be used for the geometrical SUSY breaking
We find an ISS vacuum in the quiver gauge theory for dP6 singularity
Summary
There has been a substantial progress in Model building involving the D-branes at the singularities of noncompact Calabi-Yau manifolds. We explicitly construct a compact CY manifold with del Pezzo 6 singularity and a number of conifolds such that some two-cycles on the del Pezzo are homologous to the two-cycles of the conifolds This construction opens up the road for the generalization of geometrical SUSY breaking in the case of del Pezzo singularities, where one may hope to use the richness of deformations of these singularity for phenomenological applications. There are only 8 nonanomalous combinations of fractional branes 1 We believe that these puzzles can be managed more effectively if there were more examples of compact CY manifolds with local del Pezzo singularities.
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