## [0706.3134] Triadophilia: A Special Corner in the Landscape

 Authors: Philip Candelas, Xenia de la Ossa, Yang-Hui He, Balazs Szendroi Abstract: 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-generation' manifolds with \chi=-6 that were found by Tian and Yau, and by Schimmrigk, during early investigations. It is an intriguing possibility that we may live in a naturally defined corner of the landscape. The location of these three generation models with respect to a corner of the landscape is so striking that we are led to consider the possibility of transitions between heterotic vacua. The possibility of these transitions, that we here refer to as transgressions, is an old idea that goes back to Witten. Here we apply this idea to connect three generation vacua on different Calabi-Yau manifolds. [PDF]  [PS]  [BibTex]  [Bookmark]

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Kate Land
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Affiliation: Oxford University
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### [0706.3134] Triadophilia: A Special Corner in the Landscape

Hey,
I don't understand most of it - but it looks like a pretty significant result. i.e. there is no landscape problem really as we can actually only live on a very few (3) different manifolds! This seems to be based on considering the number of particle generations you get in each manifold, and the Hodge number'. I am not quite sure why our manifold is expected to have a low Hodge number - is that just for simplicity/naturalness?

Cheers, Kate

Thomas Dent
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### [0706.3134] Triadophilia: A Special Corner in the Landscap

This is a rather excessively mathematical paper for almost everyone. They don't seem to give any physical reason why small Hodge numbers are desirable, except that there appear to be very few three-generation models at small Hodge number.
Looking at the tip of the landscape it is hard not to speculate that there may be a physical mechanism allowing transitions between what appear classically to be different vacua thereby permitting the universe to trickle down to a very special corner of the landscape, an oasis where only very few Calabi-Yau manifolds reside.
If I can try and guess what they mean: suppose that one could make transitions between different Calabi-Yaus and suppose there was an evolution mechanism which pushed the extra-dimensional geometry towards small Hodge numbers. Then the end result would be almost unique.

But the argumentation throughout the paper doesn't really address whether there is such a mechanism. Looks to me mainly like an excuse to do a lot of high-powered mathematics. Plus it reveals the fact that Candelas goes jogging with Ferreira.