# Triadophilia: A Special Corner in the Landscape

@article{Candelas2007TriadophiliaAS,
title={Triadophilia: A Special Corner in the Landscape},
author={Philip Candelas and Xenia de la Ossa and Yang-Hui He and Bal{\'a}zs Szendrői},
journal={arXiv: High Energy Physics - Theory},
year={2007}
}
• Published 21 June 2007
• Mathematics
• arXiv: High Energy Physics - Theory
It is well known that there are a great many apparently consistent vacua of string theory. We draw attention to the fact that there appear to be very few Calabi--Yau manifolds with the Hodge numbers h^{11} and h^{21} both small. Of these, the case (h^{11}, h^{21})=(3,3) corresponds to a manifold on which a three generation heterotic model has recently been constructed. We point out also that there is a very close relation between this manifold and several familiar manifolds including the `three…

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## References

SHOWING 1-10 OF 82 REFERENCES
Landau-Ginzburg String Vacua
• Mathematics, Physics
• 1992
Calabi‐Yau Manifolds: A Bestiary for Physicists
• Mathematics
• 1992
Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string
Construction of Calabi-yau 3-folds in P 6
We announce here the construction of examples of smooth Cala bi-Yau 3-folds inP6 of low degree, up to degree 17. In the last degree their constr uction is rather complicated, and parametrized by
Towards the Standard Model spectrum from elliptic Calabi-Yau
• Mathematics
• 1999
We show that it is possible to construct supersymmetric three-generation models of Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi-Yau, without section
Finding the Mirror of the Beauville Manifold
We construct the mirror of the Beauville manifold. The Beauville manifold is a Calabi-Yau manifold with non-abelian fundamental group. We use the conjecture of Batyrev and Borisov to find the
THE EXISTENCE OF SUPERSYMMETRIC STRING THEORY WITH TORSION
In their proposed compactification of superstrings [4], Candelas, Horowitz, Strominger and Witten took the matric product of a maximal symmetric four dimensional spacetime M with a six dimensional
The Pfaffian Calabi–Yau, its Mirror, and their Link to the Grassmannian G(2,7)
The rank 4 locus of a general skew-symmetric 7 × 7 matrix gives the Pfaffian variety in P20 which is not defined as a complete intersection. Intersecting this with a general P6 gives a Calabi–Yau