## Saturday, July 11, 2009 ... /////

### CERN: Weinberg on asymptotic safety

On Tuesday, Steven Weinberg gave a colloquium at CERN:

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He reviewed the history of quantum field theory, his role in it, the interpretation of current algebras and the S-matrix program, the evolution of the price of quantum field theory on the stock market, and the history of the question whether quantum field theories are fundamental or just approximate, effective theories.

Most of the things he says have become a part of the standard knowledge. Weinberg has created a significant portion of it - both as a researcher and as a communicator. While he would bet on string theory as the right theory of quantum gravity, he wants to be open-minded about the possibility that the world is a quantum field theory in the bulk - the Standard Model plus General Relativity combined in a way.

So he also discusses the asymptotic safety - the idea that the ultraviolet limit of the correct theory must belong to a scale-invariant critical surface, a condition that would return predictivity to those effective quantum field theories that are otherwise non-renormalizable, as long as these surfaces have a low dimensionality. He has showed the results of some papers that he views as partial successes.

Well, although it's politically incorrect to say, I think it is more appropriate to be closed-minded about these questions than open-minded. It's not to say that everyone must agree with me - but I am surely saying that who disagrees with me is losing her time in a dead end. In my opinion, it has been settled that quantum gravity (in dimensions 3+1 or more) cannot be a local quantum field theory in the bulk. And the removal of infinitely many types of divergences is no longer the only reason why it is so.

There has been a lot of other progress in the recent decade or so. I think that we have realized not only string theory works but even if you assumed that the right theory of quantum gravity is something else, many of the qualitative properties of string theory are necessary for any consistent theory of quantum gravity. We have a much better understanding for the detailed reasons why string theory is the only possible consistent theory of quantum gravity.

Quantum gravity cannot be described as a local field theory in the bulk because of many reasons, including

1. the infinitely many types of terms that could be added; Weinberg discussed some partial successes but I don't think that there exists any known sensible UV fixed point for gravity; after all, its non-existence was the reason why so many people began to look at Hořava's non-relativistic extension of it recently;
2. the wrong scaling of the entropy: scale-invariant field theories always have a volume-extensive entropy density and it seems impossible to guarantee that the entropy bounds will be imposed, i.e. that the black hole with its area-extensive entropy remains the record-holder for the total entropy in a volume (and therefore the ultimate stage of a collapse);
3. the information preservation during the Hawking radiation that implies that physics of quantum gravity must allow for some kind of nonlocal effects that are able to get the information out of the black hole; these effects are impossible if the causal structure dictated by a metric tensor (quantum field) strictly holds;
4. wrong trans-Planckian, very high-energy scattering amplitudes; the probability to create two particles in such a collision should exponentially decrease, as seen from general black hole thermodynamics, but that won't happen in a local theory in the bulk that is scale-invariant in the UV; the latter would lead to power laws.
I think that it is a flagrant oversimplification of the situation in 2009 to argue that a constraint on the non-renormalizable couplings would be sufficient to find or construct a consistent theory of quantum gravity. Such a program is just an attempt to solve one particular kind of problem of local theories of quantum gravity. But today, we know many more of them. Our understanding of quantum gravity is not only about some couplings and their flow: we have a truly multi-dimensional perspective on many important processes and properties of black holes, trans-Planckian scattering, and the whole picture is very constraining.

You know, the AdS/CFT correspondence describes a consistent AdS gravitational bulk physics but it also agrees with all the otherwise identified features of string theory in the bulk: it is string theory (exactly), after all. One can always compare a hypothetical "local" theory of quantum gravity in the bulk with the theories found in the context of the string theory research. And such a comparison makes it clear that every "qualitative" deviation from the rules of string theory is actually an inconsistency.

Holography won't go away: this insight of quantum gravity is not "quite" dependent upon string theory. Instead, the general principles of holography can also be justified by thought experiments and consistency considerations involving black holes and their thermodynamics. And holography with its partial implications is enough to rule out local field theories of quantum gravity in the bulk, among many other a priori conceivable scenarios.

Asymptotic darkness

There's one more way to express a similar point. Weinberg is right that the very high-energy behavior is helpful or needed to constrain the uncertain parameters seen at low energies.

The only problem is that the "asymptotic safety" theories just offer a wrong answer to the question what this very high-energy behavior actually is. The correct high-energy behavior is not given by "asymptotic safety" but by "asymptotic darkness", if I borrow a term coined by Tom Banks.

What does it mean? If you collide two particles with the center-of-mass energy strongly exceeding the Planck energy, you inevitably create a black hole. In fact, there can't be "anything else" in much of the trans-Planckian high-energy spectrum than black holes: the supply of "new physics" at these very high energies is pretty dark.

Black holes have the interesting property that the space around them - everywhere except for the singularity - looks completely empty. No complicated mess, just an empty space. Moreover, the higher energy/mass you collect, the smaller their curvature is. The number of microstates must grow exponentially with the surface, and so on.

So the very high-energy collisions are surprisingly governed by low-energy physics once again; the correct theory must interpolate between the known behavior at low energies and the same behavior at very high energies. But the details how this low-energy physics reappears at very high energies is dictated by the black hole geometry. A more detailed analysis of this situation implies that the very high-energy behavior of quantum gravity is not scale invariant but rather non-local, governed by laws that must at least qualitatively agree with those found in string theory.

Assaf Shomer wrote a detailed pedagogical explanation why quantum gravity is not a renormalizable field theory, because of the wrong number of high-energy states (black hole microstates). Thanks to onymous for the tip.