One can keep track of what is going on in theoretical physics now by taking a look at conference websites. Often after the conference they put up speaker’s transparencies or even audio or video of the talk. Some very recent examples:

Strings and Cosmology

a conference last week at Texas A and M, and

Spring School on Superstring Theory and Related Topics

at the ICTP in Trieste. Among the Trieste lectures, Marcos Marino’s notes give a nice discussion of some things you can do with topological strings. Brandenberger’s notes on “Challenges in String Cosmology” include the peculiar statement that “String cosmology does not exist because non-perturbative string theory is not yet known”. That was my impression too, but this doesn’t really explain why he is lecturing on a subject that doesn’t exist or why people devote many conferences to it.

Among the new papers appearing at the arXiv is Witten’s latest:

Parity Invariance for Strings in Twistor Space

I’m still kind of not seeing why Witten and others are so interested in this. Using strings as a dual to QCD to understand its strong coupling behavior is obviously interesting, but why is reformulating something you understand well (perturbative Yang-Mills) in terms of strings in a super-version of twistor space so interesting? The interesting thing about twistors always seemed to me that they were naturally parity asymmetric, one chirality of spinors is tautologically defined. Witten’s latest paper seems to just be showing how to get rid of this natural chiral asymmetry in this case.

Another new paper is:

The Emergence of Anticommuting Coordinates and the Dirac-Ramond-Kostant operators

by Lars Brink. The Kostant version of the Dirac operator is pretty amazing and too little known, both among mathematicians and physicists. I’m not so sure what Brink is trying to do with it leads anywhere, but there are other applications of it I’ll try and write about some day.

I think the problem with computing gauge theory at weak coupling is that, even though one can easily write down Feynman diagrams, the number of diagrams grows more or less factorially with the order in perturbation theory. Computers can be fast but they can’t handle calculations at high order when the number of graphs grows so quickly. Any technique that lets you get away with fewer diagrams will lead to better predictions.

There may be issues aside from the computational one, but this strikes me as a major advantage.

We’ll have to see how far this can be pushed. But the thing that has bothered me about it from the beginning is that, unless Witten has something up his sleeve he isn’t telling us, the most optimistic thing he seems to be hoping for is to get a reformulation of perturbative YM in terms of a string theory on twistor space. The string theory on twistor space is a topological one that seems to have nothing to do with the string theory that is supposed to unify gravity and the standard model. So this doesn’t help at all with the idea of quantizing gravity via the string. It would be kind of like AdS/CFT, where a string theory helps you understand a gauge theory. But even so, it is helping you understand not the mysterious aspect of gauge theory (strong coupling), but the weak coupling aspect, which I had thought was well understood. It was very interesting to see the comment that, in terms of computability, weak coupling gauge theory is not as well understood as I thought.

It’s pretty amazing that the twistor stuff is

actually “useful”. But the techniques of the

CSW paper look “string-motivated” to me,

not really stringy. If this “useful twistor”

stuff pans out, to what extent can that be

interpreted as a plus point for string theory

per se?

Hi Mark,

Thanks for writing this, that’s very interesting to hear. I didn’t know that tree-level perturbative YM amplitudes could be that hard to compute, so didn’t realize that Witten’s results would be so useful. The fact that abstract theory involving strings and twistors is leading to phenomenologically important calculational techniques is pretty amazing. Will be interesting to see what happens with loops, presumably there are a lot of people working on that now!

Hi,

I am replying to Peter’s comment that

“It wasn’t clear whether the twistor ideas really help do any

calculations these people [at the Tevatron and LHC] care about.”

Here at the KITP we’ve had a workshop on collider physics for the

past two months, and all of the experts in exactly this field have

been at hand. It’s hard for me to overstate the excitement,

in particular of Zvi Bern (workshop organizer and undoubtedly

one of the leading experts on perturbative QCD calculations).

Calling the paper hep-th/0403047 a “home run”, Zvi said that

this is exactly the technology they’ve wanted for more than a

decade. For more, see Zvi’s colloquium at

http://online.itp.ucsb.edu/online/colloq/bern1/

To give an example, consider the 8-gluon amplitude with

helicities ++++—-. As recently as March 2, 2004, one could

have invested many, many months of effort into calculating this

and written a lengthy paper on it (7-gluon amplitudes appear in

a 40-page paper in 1990). After March 3, I (and independently

David Kosower and I think Zvi as well), spent part of a lazy

afternoon writing this amplitude down “just for fun”.

It’s only 44 CSW diagrams, versus 34,300 Feynman diagrams.

People who write Monte Carlo programs for the Tevatron and LHC

need to know these (and other) amplitudes in order to get a better

handle on experimental backgrounds. Zvi said that these programs

would all have to be rewritten now to use the fantastic

new CSW technology. So, quoting from the mouth of an expert: Yes,

people care!

Of course, so far Witten’s new technology has been only applied

at tree level. The REAL (practical) payoff from twistors will come

from finding some way to apply this technology to loops, where the

perturbative QCD calculations start getting VERY hard.

I inserted the word practical above to emphasize that there are

other, more theoretical payoffs from Witten’s work (such as some

interesting new ideas on S-duality for topological strings, as

well as other ideas surely to be discovered), but I specifically

wanted to limit my reply to your question in the context of the usefulness

of twistors for QCD calculations.

Mark

Oh no! Now I’m going to have to start reading Jacques Distler’s postings about how to keep cranks from spamming the comment sections of one’s weblog. Maybe Jacques can explain how to filter out just physicists from Harvard with Junior Fellowships.

As usual, Lubos is devoting his efforts to insulting others while avoiding the issue under discussion. He’s still not answering the question I asked him when Witten’s paper first came out: “What good is this new connection between perturbative YM and strings on super-twistor space?”

The claim that “twistors used to be nearly as popular as string theory is nowadays” is pretty weird. One could check this out with the SPIRES database, but I’d guess that in any of the last 20 years there have been 10-100 times more papers about string theory than the number written about twistor theory in the year of its peak popularity, whenever that was. Given Witten’s paper and the complete lack of any other ideas for string theorists to work on, maybe 2004 will be the year of the peak number of twistor theory papers.

Amazing, Peter! If I did not see this, I would not be able to believe that you are able to establish your own blog. I wonder whether you will erase this comment from your page, even though the people who don’t know yet can learn that you are a bitter and intellectually limited person.

Recall that you were saying on sci.physics.research that this twistor stuff is beautiful, as soon as Witten started, and it’s great that the people in the field would have to follow Witten. Your comments about physics are not not obsolete, silly, and annoying, but as we see now and again, they are also internally inconsistent.

Twistors used to be nearly as popular as string theory is nowadays, and Penrose himself believed that it was important to investigate this unusual description of the Minkowski spacetime because it might teach us something about quantum gravity.

His dreams have not been realized because their research was always very primitive. In the best case, it allowed them to calculate various things in a new way – for example the moduli space of instantons (ADHM) was first obtained using these methods. The twistors are now studied seriously, i.e. by string theorists, and all the potentially good and useful ideas and notions (such as D-brane instantons etc.) can be applied.

Twistors make the left-right parity symmetry very obscure, and therefore an explicit proof of this symmetry was (and is) very desirable. Witten’s proof of this fact (and our earlier proof in Berkovits+Motl, as well as the proof in the paper by Volovich et al. a day later) is perhaps not a new revolution in physics, but it is certainly an interesting result – definitely more interesting than anything that you have done during the last 12 years, and therefore I would expect a little bit of respect from you, especially if you are – please accept my apologies for being straightforward – such a loser.

I saw that Witten gave a talk about this stuff to the workshop at the KITP where some people are doing perturbative QCD calculations necessary to understand backgrounds at the Tevatron and the LHC.

It wasn’t clear whether the twistor ideas really help do any calculations these people care about, and they are the only ones I can think of who might be able to use better ways of doing perturbative YM computations. I’d guess Witten mainly hopes to get new insight into the relation of string theory and gauge theory out of all this, but I don’t see anything that promising here yet.

Brief comment on the twistor stuff, but I don’t know very much: I was visiting Harvard yesterday (as I might go there for grad school) and Nima Arkani-Hamed explained a bit about this to me. Apparently scattering amplitudes in Yang-Mills theory turn out to have much nicer forms than one sees in doing the perturbative calculation. My impression is that you might hope to calculate things more easily this way — you don’t have to sum as many graphs — and also maybe certain analytic properties are easier to understand. But, I’ve only heard this briefly explained, so I’m not too sure of what the advantages are. People do seem convinced that this is useful.