## Thursday, May 28, 2009

### Don’t modify gravity: understand it

Mark Trodden and Dmitry Podolsky wrote about a gravitational conference in Cleveland, Ohio that they have attended.

Some talks have focused on experimental tests - but for these tests to make sense, there should also exist a rational or semi-rational reason to expect some deviations from the theories we use today. And people have had different opinions about this point, as we will see, even though only one opinion is correct. ;-)

Dmitry reported that Newton's law is now known to be valid at all distances above 56 microns. He is linking to some interesting animations of high-velocity collisions of black holes and the resulting radiation. And finally he tries to propagate some confusion about the quantum coherence in the black hole context - a confusion that he has already tried to share with Samir Mathur who has promoted fuzzballs (see also his recent short paper about the tunneling rates into the fuzzball states).

In Dmitry's text, De Sitter space is finally described as being analogous to a black hole, except that the "black hole interior" is outside the cosmic horizon and the cosmic horizon depends on the observer, unlike the black hole event horizon. The identification of microstates of a de Sitter background remains completely unknown and it is questionable whether such a problem can ever be well-defined at all.

Nima's talk

But I have borrowed the title from Nima Arkani-Hamed who has also noticed that people don't seem to have a sufficient appreciation for the deep wisdom of principles underlying gravity that have already been uncovered.

Nima has invented lots of models, many of which are very unlikely, so he can surely be viewed as an impartial judge when he says that most modified models of gravity that are being proposed are ill-conceived crap. And be sure that they are. Instead of modifying gravity, you should better understand it first! ;-)
See Dmitry's second article about the conference for details about Nima's talk.
Your humble correspondent completely shares this viewpoint. In some sense, we already know enough: we just can't quite organize our knowledge and all the far-reaching relationships in our minds too well. These theoretical bridges are sometimes too vast for our little brains.

Nima thinks that people should try to find a holographic description of the flat space, analogous to AdS/CFT. Well, this is surely a nice task except that I feel that in some sense, we already have it. The flat-space counterparts of the CFT correlators are clearly the S-matrix scattering amplitudes and we do know how to compute them, perturbatively or otherwise: there is probably no simpler method to do so than the methods that have been found.

The most radical things one can get in this context are e.g. various reformulations of the S-matrix in the twistor space, see e.g. the recent exciting paper about the perturbative N=8 SUGRA by Nima and others.

In other words, I feel that the difference between the "bulk" and "boundary" description is much less "qualitative" in flat space than it is in the AdS space whose boundary is really "localized", unlike the "scri plus". It means that Nima's program, while surely interesting, could turn out to be somewhat vacuous and pretty much solved because the holographic duality has "less beef" in the flat space. A different task is to deduce the flat space S-matrix from the CFT correlators of an AdS background: this task is certainly non-trivial and probably too difficult, in fact.

There are many similar projects that deserve the attention, in my humble opinion.

For example, people should try to identify the correct black hole microstates - or fuzzballs - in new backgrounds, especially in the Rindler space, another representation of the flat space. I have been working on this problem for some time, with incomplete results (but knowing how to prove the Bekenstein-Hawking formula for general large black holes by summing over microstates). The Rindler space is much more universal than e.g. the LLM bubbles with S^3 x S^3 in them: locally, it is a part of any large enough black hole. And it could be understood in a new way, using the stringy (or AdS/CFT or Matrix-theory) methods.

But this is really about the conventional picture of gravity and the approaches to solve the remaining enigmas of the information loss paradoxes, not about modifications of gravity.

So much like your humble correspondent, Nima expects the tensor-scalar diff-invariant, locally Lorentz-invariant gravitational theories coupled to matter to be the only possible local effective classical limit of any consistent theory of quantum gravity. I am adding more words to his mouth than what I've seen but I think that he would subscribe to this somewhat carefully crafted proposition. Quantum mechanics surely adds a lot of interesting details about the dynamics, the microstates, and the non-locality - but once you get to the classical limit, its form seems to be universally determined.

He argues that the conventional general relativistic form of the field-theoretical limit is necessary for holography to hold. I haven't heard the talk but I think he's right. Holography seems to be a damn too shocking, unusual, yet universal and important feature of any consistent theory of quantum gravity. For non-AdS backgrounds, holography is not really fully well-defined, but even if you reduce it to the entropy bounds (proportional to areas), they're still shocking from the viewpoint of generic field theories.

The holograms must still look "real", so the corresponding bulk description is kind of constrained. And sub-Planckian distances must be unphysical because the heavy gadgets needed to measure them inevitably collapse to black holes which are again larger than the Planck length: a specific type of non-locality.

A commenter at Cosmic Variance, AdSMan, says that "everything goes" because any theory with an AdS-like solution is likely to have a dual, boundary description. Well, it depends on your definition of "AdS-like solutions". Good enough AdS-like solutions can only exist in theories of Nima's (or Einstein's, to be more precise) kind.

For example, if we talk about "proper" AdS/CFT, the boundary theory should be conformally invariant. This symmetry gets mapped to the AdS isometries of the bulk. The latter symmetry locally acts on a region by an action that includes the local Lorentz symmetry which is therefore an inevitable part of the picture. In particular, there can't be any preferred slicing of the bulk because that would make the existence of the boundary dual impossible.

For example, Hořava-Lifshitz gravity is manifestly non-holographic because of its preferred slicing (and other flaws). A point on the holographic screen is inevitably and non-locally associated with a whole (co-dimension zero) region in the bulk which is incompatible with the existence of preferred slices of the bulk. I am confident that whoever messes up with the dimensions in this counting will destroy holography completely.

While the most impressive evidence exists for the purest classical AdS/CFT duality, especially for the case of the N=4 gauge theory, one can accept that the duality may be weakened a bit, even to non-AdS/non-CFT theories. You may think about the cascading gauge theories, for a refreshingly new example. But the more generic the two sides are, the less uniquely well-defined they are (especially the bulk side which has no lattice formulation etc.) and the less certain we are about their equivalence. Moreover, the success dramatically decreases if you get to theories where the conformal symmetry is broken more brutally than "softly" (i.e. just in the infrared).

Similar observations hold for the diffeomorphism symmetry. In AdS/CFT, the bulk theory must inevitably have some kind of diffeomorphism symmetry whenever the stress-energy tensor of the boundary theory is conserved. In fact, the stress-energy correlators on the boundary are linked to the scattering of purely physical degrees of freedom of the graviton. Consequently, we know that both local Lorentz symmetry as well as the removal of the unphysical components must occur in the bulk theory.

You know, the Einsteinian theories, even when extended to their quantum stringy completions, don't seem to solve certain problems, especially the cosmological constant problem, in a terribly satisfactory way. But I think that in their attempts to solve this problem "non-anthropically" (and we don't know for sure whether this goal is actually promising), almost everyone is throwing the baby out with the bath water. Their modifications of gravity are just too primitive and too manifestly inconsistent.

Needless to say, things get even more radical if people are trying to motivate their new theories by a desire to re-explain some phenomena currently attributed to dark matter. A lot of recent observations indicate that dark matter is almost certainly real - and we have learned to consider new particle species to be a mundane phenomenon - so these attempts to build gravity "from the scratch" could be just way too crazy, especially if the results look so primitive in comparison with the theories building on Einstein's heritage.

People will be trying many things, anyway, but I would bet that the success will come from those who try to understand gravity rather than to modify it.

And that's the memo.