Dawn of the dS/CFT: Higher Spin Realization of the Correspondence

[mitchell porter]

In recent months, the possibility of a dS/CFT correspondence, analogous to the famous AdS/CFT correspondence, was discussed here several times. It was announced at Strings 2011 that a realization of dS/CFT has been discovered and that a paper would be coming out last month. Now, at the end of August, it has finally arrived:

http://arxiv.org/abs/1108.5735

Higher Spin Realization of the dS/CFT Correspondence
Authors: Dionysios Anninos, Thomas Hartman, Andrew Strominger

Abstract: We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on the spacelike boundary of dS at future timelike infinity. The CFT is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT flows under a double-trace deformation to an interacting CFT in the IR. We argue that both CFTs are dual to Vasiliev dS gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and boundary correlators in the proposed duality relating the O(N) model with Vasiliev gravity in AdS.

Perhaps the first order of business for anyone wanting to understand the paper, is to understand why the dual CFT lives on the future boundary, rather than the past boundary or some combination of the two.

Coincidentally, the day also brings http://arxiv.org/abs/1108.5921" . Of course the latter doesn't have an "uplifted CFT" to go with the constructed de Sitter solution, but that must be on the agenda now.

 

[marcus]

This is intriguing. I don't understand the business of defining the CFT on the future infinity. It always seemed to me that a dS spacetime doesn't have any boundary (I don't think we count the observer's event horizon as one in this context).

So as of now I don't understand what they are doing, but maybe I will later.

The future of a dS has no fixed size, maybe the fact that the fields you want to define on the infinite future are conformal is the key enabler.

I put this in the Loop gravity bibliography. I think it may turn out to be useful to other research gambits besides string. It is the kind of thing Laurent Freidel is apt to have something to say about. Thanks for pointing it out!

 

[dhillonv10]

You beat me to it :) i was going to make a post about the paper in the morning. Now what'd be really interesting is to see how they generalize this work done to a string theory in the bulk instead of Vasiliev gravity.

 

[mitchell porter]

Marcus, I suggest Jörg Frauendiener's review http://relativity.livingreviews.org/Articles/lrr-2004-1/" , especially section 2.3. The conformal boundary consists of a set of "points at infinity", each of which is the endpoint of an equivalence class of null geodesics. The physical space-time is topologically an open set; the addition of conformal infinity creates a closed set, and then you can conformally rescale the physical metric to get a new metric defined on the closed set, including on the boundary at conformal infinity.

One of the intriguing things about these correspondences is that the physical infinity - the infinite distance to the conformal boundary - corresponds to an infinite divergence in the boundary CFT. You may have a calculation in the bulk (dS here) where, e.g., you are calculating the action of a configuration of bulk fields which is infinitely extended in space or time, and this corresponds to a calculation of quantum correlation functions in the CFT that is defined wholly within the conformal boundary (the "fictitious" set of points at infinity that was added to the bulk space-time). (The two calculations are related by the boundary conditions of the bulk fields at infinity; the bulk fields at infinity become sources in the quantum field theory on the boundary.) The action of that infinitely extended bulk configuration will be infinite, and the correlation functions in the CFT will be divergent (infinite), but they can both be renormalized, and http://arxiv.org/abs/hep-th/0101026" . For example, introducing an energy scale cutoff in the CFT corresponds to truncating the bulk space-time rather than letting it extend to infinity.

So in this case the "infinite future" of the de Sitter space should correspond to UV divergences in the dual Euclidean CFT.

As for the business about past and future boundary conditions... http://arxiv.org/abs/hep-th/0106109" .

But the ultimate reason they focus on future boundary conditions may just be the desire to match reality. "Our own universe is unlikely to have an anti-de Sitter boundary, but may well have a de Sitter (dS) boundary in the far future." And they may have something like Hawking's no-boundary proposal in mind for the start of the universe.

Vikram, a generalization to string theory may be some time in coming. See the footnote on page 2. When the paper took so long to come out, I wondered if they were going to cover more than the promised example, but they didn't even consider the extension of Vasiliev's theory that has fermions in it (which in AdS http://arxiv.org/abs/hep-th/0304217" ). In the long run, I think dS/CFT may be even bigger that AdS/CFT, because it may provide the right language to talk about solutions of string theory with an evolving background. But right now they're still struggling to make conceptual sense of this very first example.

 

[atyy]

Is higher spin gravity only a toy theory, or does it have phenomenological potential? I thought it doesn't even reproduce Einstein gravity. But http://arxiv.org/abs/1007.0435" say "In fact, by putting more emphasis on the AdS/CFT correspondence, one may provide further arguments [21] why higher-spin gravity is a natural framework for seeking ultraviolet completions of general relativity. Ordinary general relativity together with various matter couplings (and without exotic vertices) may then appear at low energies as the result of the dynamical higher-spin symmetry breaking mechanism induced by radiative corrections proposed in [21], provided that the induced non-critial mass-gaps grow large at low energies."

 

[mitchell porter]

I had assumed that it incorporates the equivalence principle, just on the grounds that it has a spin-2 field. Maybe the real issue is, how to see that Vasiliev gravity has diffeomorphism invariance. There's a paper saying that http://arxiv.org/abs/1106.4788" ! - so the "quantum geometry" here may be a little unusual - or maybe the paper is wrong and the gauge invariance comes back when you look at all the higher spins, not just spin 3.

As for phenomenology, http://arxiv.org/abs/1011.4926" suggest that there are a vast number of Vasiliev-like theories that can be constructed from free field theories on the boundary. So one could begin by trying to understand what sort of boundary theory gives you, say, Yang-Mills in the bulk.