# Is our universe a 2+1D superconformal field theory?

If our universe comes from a flux compactification of string theory over 6 dimensions with a nonzero flux, then it can't be continually deformed to another compactification with zero flux as the total flux is a topological invariant. The cosmological constant of our universe is positive, which in string theory means it is a metastable state. The stable vacuum for a flux compactification in string theory is a BPS compactification with negative cosmological constant.

What if our metastable observable universe is actually embedded in a larger stable anti de Sitter background? An inflating metastable or slowly rolling or chaotically inflating patch of this asymptotically AdS universe inflates to our observable universe. By the AdS/CFT correspondence, our universe can be described by a superconformal field theory in 2+1D with no gravity.

Is there any flaw in my reasoning?

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Topological invariants become topological quantum numbers in the quantum version of the theory. As such transitions between states labeled by different topological quantum numbers are not prohibited, so the argument of your first line (can't be continually deformed ...) does not stand. – user346 Mar 3 '11 at 16:17
Let me clarify a little bit. Transitions between different flux vacua with different values of the CC can be described by instanton transitions that correspond to spontaneous membrane nucleation in 4D. In the original Bousso-Polchinski paper this bubble nucleation is exactly the dynamical mechanism that populates the landscape. Vacua with small positive vacuum energy $\Lambda$ can be pretty long-lived because the tunneling amplitude is roughly $exp(-1/\Lambda)$. – stringpheno Mar 3 '11 at 16:49
Vacua where all geometric moduli are stabilizad without fluxes have also been constructed, e.g. see here arxiv.org/abs/1102.0011 , and from the phenomenological point of view such fluxless vacua may actually be more relevant for the real world because they may lead to a more natural explanation of the gauge hierarchy problem. – stringpheno Mar 3 '11 at 16:56

No-one has dared to answer this question yet. So let me get the ball rolling. It seems that there are a large number of problems to be solved for this proposal to work, but I'm not aware that any of these problems are definitely unsolvable (though that might just be my own ignorance).

(1) This is to be an AdS4/CFT3 duality, then we are dealing with M-theory (a stack of coincident M2-branes) on AdS4 x a 7-manifold, or equivalently, Type IIA string theory (a stack of coincident D2-branes) on AdS4 x a 6-manifold. As pointed out in a surprising dialogue from 2005, we immediately face the problems that (i) there's far too much supersymmetry for a realistic model (ii) the 7-manifold is as big as the AdS space. I don't know what to do about the latter problem, but for the better known AdS5/CFT4 duality, we have many variations on the original construction in which supersymmetry is broken a little or a lot, so let us suppose we can do that with AdS4 too.

(2) In order to get the universe we see, a local or temporary patch with de Sitter geometry has to form within the AdS space. I have no idea how that would be represented in terms of the boundary CFT. In fact, I cannot even find a known CFT dual for any AdS space which is used as the basis for a construction of dS space in string theory. The dialogue above mentions a quest for CFT duals of the AdS spaces appearing in the KKLT paper from 2003; it doesn't seem that they are known yet, even in 2011. Embedding de Sitter space in the CFT framework is an even bigger challenge and figuring out how to do so would be a breakthrough.

(3) The KKLT construction adds anti-D3-branes to the AdS space, to lift it to dS, but they were working in IIB string theory, and it looks like the gravity theory in our AdS4 space will be IIA. Fortunately, there's an alternative mechanism available for IIA.

(4) We also have to get the fields of the standard model out of this somehow. I'll mention just one problem here, and its potential solution: "the inclusion of particles in the fundamental representation of the gauge group, i.e. quarks. Since AdS geometries arise as near-horizon limits for coincident branes, the dual field theories have only adjoint matter. The same is true for deformations of AdS. It turns out that fundamental representations can be introduced by including appropriately embedded probe branes."

So there you have it. There's a whole raft of problems that would have to be solved to turn AdS4/CFT3 into a source of phenomenological and cosmological models. Some of them may already be demonstrably unsolvable, for technical reasons I don't appreciate, while at least one other basic element of the plan (dS/CFT) is a major unsolved research problem of string theory. Good luck!

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Let's be clear about what your hypothesis would entail. There is an expanding FRW patch in our current phase with a positive cosmological constant embedded within a phase with a negative cosmological constant which is asymptotically anti de Sitter. Draw an enclosing 2D spatial surface in our FRW patch larger than the cosmological horizon radius. It generates a time inverted trapped null surface. However, extremely large enclosing boundaries must not generate inverted trapped null surfaces because spacetime is asymptotically AdS. In between is an apparent horizon boundary. Penrose-Hawking theorems apply within the interior of this apparent horizon boundary because the spatial exterior is noncompact (which is why closed universes need not have big bangs). Your hypothesis would mean we're living within an extremely large white hole. Similar arguments apply to speculations of us living in an asymptotically flat phase with a zero cosmological constant.

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