Holography and Calabi-Yau compactifications

[crackjack]

Holography separates the space of non-gravity (gauge) and gravity (string) theories into boundary and bulk. As I see it, CY compactifications do no such separations. So, aren't they fundamentally inconsistent with each other?

I also see more and more string theorists starting to believe in the general holographic conjecture that there is a string theory for every gauge theory. But they look at this duality more as look-up table for individual gauge theories (like in QCD, condensed matter etc). Why has holography not gained *enough* popularity in the context of unification? In this unification context, CY compactification still rules the field.

If there are strong reasons to believe that holography might not be best suited for unification, can both ideas - holography & CY compactifications - coexist?

 

[petergreat]

It seems to me that in AdS/CFT the bulk is compactified on spheres. Does Calabi-Yau compactifications of string theory have CFT duals?

 

[smoit]

There are so-called Klebanov-Strassler solutions, also known as "warped deformed conifold", that have CFT duals http://arxiv.org/abs/hep-th/0007191" . These manifolds are Calabi-Yau, up to a conformal warp factor, and are typically regarded as describing some local geometry that looks like a long throat glued to some compact Calabi-Yau bulk.

 

[crackjack]

Thanks smoit. I was also informed of these strings on conifolds with warped throat dual to cascading gauge theories, a little after I posted here. I also found the following lecture notes on these:
http://arxiv.org/abs/hep-th/0205100
http://arxiv.org/abs/hep-th/0505153

Also:
http://arxiv.org/abs/hep-th/0502113
http://arxiv.org/abs/hep-th/0503079 (has an attractive title)

So, it seems some aspects of conventional CY compactifications, with some additions, are compatible with holography.

@petergreat: Yes, it seems so. The lecture notes above have more explanations.

 

[S.Daedalus]

I also see more and more string theorists starting to believe in the general holographic conjecture that there is a string theory for every gauge theory.

Just as an aside, is the opposite -- that there is a gauge theory for every string theory -- generally thought to be true, as well?

 

[fzero]

Just as an aside, is the opposite -- that there is a gauge theory for every string theory -- generally thought to be true, as well?

It's fairly straightforward to extend the AdS/CFT correspondence to $$N=1$$ superconformal theories in 4d. The dual theory to these is IIB theory on $$\text{AdS}_5\times X_5$$, where $$X_5$$ is a so-called Einstein-Sasaki manifold. The properties of an Einstein-Sasaki manifold guarantee that the cone over it is a noncompact Calabi-Yau manifold, i.e.

$$ds_6^2 = dr^2 +r^2 ds_{X_5}^2$$

is a Ricci-flat metric.

There are examples in the literature of nonsupersymmetric correspondences that are understood to some extent. I'm not particularly familiar with the details, but some of these examples involve nonsupersymmetric orbifolds of supersymmetric theories or perhaps the geometry of tilted brane configurations. Examples like that are probably the only ones where you have much of a dictionary on both sides.