Most of the lectures from this year’s Jerusalem Winter School in Theoretical Physics are now available online. David Gross was the main organizer, and the choice of topics reflects his point of view on what is interesting these days in theoretical physics. The landscape and anthropics were pretty much completely suppressed (although Michael Dine did manage to slip in a mention, his slides are here). The idea of “string phenomenology”, i.e. getting the standard model out of a unified string theory and saying something about particle physics has fallen by the way-side.

In his summary talk (given at the beginning of the conference), Gross described the same point of view he has promoted for many years now. He thinks something is missing in our understanding of string theory (“we don’t know what string theory is”) which will somehow fix the failure of ideas about string theory unification. This failure though doesn’t matter anyway, since he now claims that string theory = QFT, based on gauge-gravity duality, and thus “string theory cannot be killed”. It’s very unclear how this equivalence claim fits together with the “we don’t know what string theory is” claim, since we do know what QFT is (we have a very good understanding of the Standard Model). It seems that Gross would like to define away much of the troubles surrounding string theory.

One idea that Gross has favored for a very long time is that string theory is telling us that we must give up our usual notions of space and time, only recovering them in some limit. Two of the series of lectures at the school were about rather grandiose attempts to do something along these lines. There were three lectures by Erik Verlinde on his ideas about “emergent gravity”. I continue to not be able to make much sense of this program. He invokes the reasonable idea that gravity is an effective long-distance force due to unknown fundamental degrees of freedom, which may very well be true. But he doesn’t seem to have anything specific to say about the fundamental degrees of freedom strong enough to get anything new out of this. There were some ideas at the end about dark matter and dark energy, but it was unclear to me whether these go anywhere.

Much more interesting was Nima Arkani-Hamed’s series of lectures on *Scattering Amplitudes and the Positive Grassmannian*, which he said could have been titled “How you get spacetime from the permutation group”. The first lecture started with a philosophical introduction that he said he would limit to 5 minutes, but which went on for 40. Only the first two lectures are now online.

Unlike Verlinde’s ideas, here there are very specific calculations involved. The starting point is recent progress in understanding perturbative amplitudes for N=4 SYM (and for more general gauge theories). These involve working in twistor space, and more generally working with variables such that locality and unitarity are no longer manifest. The basic mathematics and geometrical principles at work are quite different than the standard formulation of gauge theories in terms of local variables and gauge symmetry. As usual, Arkani-Hamed makes wildly enthusiastic claims. In this case, he claims to have finally found a remarkable new understanding of the subject, based on some combinatorial objects and dramatic new mathematical ideas. He does note that this still hasn’t been written up, and that it’s the third time in the past year that he has thought he had things understood, with the last two times not working out.

I’m quite curious to see where this all goes, although I confess that I’m planning on waiting a while to try and follow the details, since this is clearly very complicated work in progress, and a 4th or 5th iteration of the fundamentals may very well be on its way over the next few months. Arkani-Hamed is talking to mathematicians, including his colleague Pierre Deligne at the IAS, and says that he is moving from the old-style of Atiyah mathematics to a new-style of Grothendieck-based mathematics. I’m not sure what this means, but suspect that Atiyah’s ideas are still in there (Grassmanians, twistors and toric varieties are subjects he has been very much involved with), and that the Grothendieck business may be an artifact of talking to Deligne, who comes from that tradition. Grothendieck was the master of generality, so his ideas can be applied to a very large fraction of mathematics.

Also lecturing on amplitudes, from a much more down-to-earth point of view, was Zvi Bern. For more from both Bern and Arkani-Hamed, see the program of the recent Amplitudes 2011 conference in Michigan. Slides from Arkani-Hamed’s talk give a better idea of what he is up to, and Bern’s slides contain his summary comments about the state of the subject. He emphasizes the connections between amplitude calculations and other fields and seems to be arguing for more attention to practical results, less to “symmetry, beauty and aesthetics”. He worries that while “Today our field is one of the hottest ones around”, the long-term future is less clear: “Is our field just another (albeit long lasting) fad?”, so attention to results relevant to the rest of physics is important for long-term health.

Lots more “Amplitudes” conferences on the way, including Amplitudes 2012 in March, a conference at the Newton Institute in April, and one at the IHES in December.

“He does note that this still hasn’t been written up, and that it’s the third time in the past year that he has thought he had things understood, with the last two times not working out.”

I happened to check the Arxiv yesterday to see if he had published anything lately. I was wondering if he took 2011 off. Hopefully the third (or fourth) attempt at understanding the twistor approach works out.

Of course, both Nima and Zvi are just returning to the Analytic S-matrix program… whose biggest success has always been string theory 🙂

It’s very unclear how this equivalence claim fits together with the “we don’t know what string theory is” claim, since we do know what QFT is.There is a class of conjectured correspondences between an established theory and a conjectured theory. Is that so hard to swallow?

Since AdS/CFT was invented, we have discovered a large class of new conformal field theories which have no known Lagrangians, but are defined solely in bulk space via a gravitational action coupled with certain matter fields. In this case, our understanding of the particular QFT is limited, but it becomes transparent when we look at it from the gravity/string side, in stark contrast to what you said above.

anon,

I’m well aware of the conjectured set of correspondences. My point is just that Gross is engaging in a bit of sophistry here. He’s trying to avoid acknowledging the failure of unified string theories (“string theory can’t be killed”) by saying that now “string theory” is identical with a well-established, successful QFT, the Standard Model. But if you ask what’s the string theory equivalent to the SM, you find it’s one that “we don’t know what string theory is” applies to. You can legitimately make the argument that “string theory” is now a set of ideas deeply related to our ideas about QFT, but the controversial question is whether these ideas provide a fundamental theory or not, and Gross is playing word games with this question.

This was just a winter school. It is not necesarily relevant for the development of String theory.

@anon:

it is statements like this that make me queasy about the whole applied AdS/CFT business. AdS/CFT is well defined (and well checked) for certain, mostly highly supersymmetric, examples. I do not accept that writing down (say) the Einstein-Hilbert action plus a U(1) gauge field plus a scalar field with an AdS minimum defines a CFT. We generally don’t know whether the bulk theory exists as a limit of string theory, whether there are any subtle instabilities, whether the naive rules of AdS/CFT work here, etc etc….

In the last two minutes or so of the video of David Gross’ opening talk, Gross answers a question, arguing that string theory is the ultraviolet completion of quantum field theory. He says that our modern understanding of QFT is in the Wilsonian sense; and that is understood only in the infrared.

Anonyrat,

This kind of argument by Gross is much trickier than he is making it sound. He won a Nobel prize for showing that non-abelian gauge theories are asymptotically free, so extremely well-behaved in the ultraviolet (it’s in the infrared that they’re hard to understand). There is no need for string theory as an ultraviolet “completion” of QCD; if it’s of any use in QCD, it would be in the the infrared.

The “ultraviolet completion of a QFT” argument only makes sense if you insist on coupling your QFT to gravity and quantizing gravity. Then you have non-renormalizability problems (unless Zvi Bern shows some version of supergravity is finite and you can use that…), which the string theory “ultraviolet completion” might solve for you. But, as Gross well knows, string theory unification opens up multiple cans of worms, ones he hopes to argue away with “we don’t know what string theory is”. This is not a rock-solid argument…

Peter, just to clarify: There is no problem with QCD in the infra-red, all IR divergences cancel when you calculate a cross section or other physical observable. There is no need for help from string theory, or any other new physics, here. There are UV divergences, which are removed by renormalisation of course. We don’t worry about this, because we know that QCD is just a low-energy effective theory, and this is how low-energy effective theories behave. It is an open question as to what is really going on at high energy. This doesn’t matter for day-to-day QCD calculations, thanks to renormalisability.

I’m sure you are in agreement with this, just thought I’d spell it out.

pah,

Actually I’m not in agreement at all. QCD is asymptotically free, which means that its ultraviolet behavior is perfectly under control. Put it on the lattice and you know exactly how to define the limit as the lattice spacing goes to zero. There are no problematic divergences (non-asymptotically free theories like QED are a different story). In the infrared, there’s no problem defining the theory, but it is a long-standing hope that some sort of string theory provides a useful effective description.

Right, you’re saying that string theory (or whatever) might help us understand low-energy, non-perturbative QCD, which is otherwise well-nigh impossible to calculate with. And that would be great. But it would still just be the QCD Lagrangian, so nothing would have changed in that respect, it would “just” be an effective description of QCD in this domain.

At high energy the theory (QCD) actually breaks down and requires renormalisation to make any sense. The property of asymptotic safety does not change the fact that scattering amplitudes are UV divergent. Renormalisation can be thought of as taking from experiment (in the form of the measured coupling and masses at a certain scale) the parts of the calculation that your theory does not predict – basically the parts which depend on what is going on at very high energies. It is here where new physics must come in, hence all this talk of UV-completion.

pah,

No. QCD is not “asymptotically safe”, it is asymptotically free. The theory does not break down at high energy, quite the opposite: it becomes more and more weakly coupled and under better and better control. Any divergences in your perturbation theory calculations are artifacts of how you do the calculation and we understand how to deal with them. You need to learn more about the renormalisation group.

Think about how lattice gauge theory calculations in QCD are done. You take the continuum limit by taking the coupling to zero as you take the lattice spacing to zero, according to the renormalisation group, and this gives a well-defined limit, with non-trivial infrared behavior, but trivial ultraviolet behavior. This is not yet rigorously mathematically proved (that’s one of the Clay million dollar problems), but all numerical and other evidence is that this is how the theory works.

In my humble, uneducated opinion, the line of thought of Arkani-Hamed, Cachazo, Hodges, Mason, Skinner and friends is very exciting indeed, and I expect it to be more so over the next couple of years.