Gravity is a fine classical field theory, but it is easy to see it cannot be treated as a QFT, since it cannot be renormalized. Just try to calculate almost anything with the usual formalism of QFT, you’ll get nonsense.
If you redefine what you mean by either gravity or QFT, all bets are off.

There are less mechanical ways to state the problem, for example the lack of decoupling in gravity. Decoupling is at the heart of properly defining QFT via RNG flows etc., but in gravity heavy objects cannot be treated as “fast” variables a la Born-Oppenheimer, because they are simultaneously strongly coupled, exactly because they are massive.

One issue in QFT which may be interesting is its applications to highly dynamical situations, such as non-equilibrium processes. I have a feeling that a lot of the Lorentzian issues one encounters in string theory lately will already be manifested there, and there is probably a useful body of knowledge out there.

As nobody else starts I’ll take the lead to list a couple of field theory questions: And I start with a non-field theory question: Is gravity just a field theory? I.e. is there really an intrinsic difference between gravity and ordinary field theories or is it just another field theory with spin 2 fields and a large gauge invariance. People often take it for granted that there is some special magic with gravity but I am not yet convinced this is the case. For example these peopl e point out that it is remarkabel that AdS/CFT connects a field theory with a gravitational theory. But it seems one could also come up with similar purely field theoretic examples. Maybe you are going to say that gravity has holography but in that case please define holography precisely and explain why this cannot be a property of a field theory.

There are of course millions of questions to understand theories without susy and non-holomorphic properties of N=1 theories beyond the first couple of orders of pertubation theory, confinement being just one of them.

I think what is not such an interesting question (and I believe even many of the more formal people agree) is to show that there are interesting field theories in the mathematical sense (e.g. Whiteman or Haag-Kastler axioms): My understanding is that the only examples where this has been worked out are free theories and rational CFTs in 2D but I think nobody has doubts that 4D gauge theories (maybe supersymmetric) fulfill these (or some reasonably adopted) axioms: You could start from the lattice (once you solved the problem of having chiral fermions and susy in this case) and then attempt to prove that the continuum limit exists and has nice properties (covariance, locality, positivity). Technically, this is a very very hard problem but I doubt that anybody believes that there serious problems there.

I have the impression that there are a lot of interesting things still to be learned from the connection between field theories and topology (and these might again have brane interpretations) but maybe Peter can comment on this.

Please comment and continue!

Thanks for the reply, Clifford, I agree with everything you say. I should say welcome as well- it is already clear that one has no chance of getting anything done at the face of 5 (!) of you guys…

And probably plenty more than that. You can also check out Freddy’s slides at Strings 05.

Moshe, link to some representative papers, please!

-cvj

I’m very glad that you’ve decided to participate in this weblog. Without naming any names, much of the public face of string theory in recent years has consisted of people who are either uncritical over-enthusiasts and/or intent on personal attacks on anyone who has anything critical to say about what is going on. On the other hand, almost all seasoned string theorists I meet or know personally have much more moderate and reasonable views, and in discussions with them I generally find we agree about most things.

Often our disagreements come down just to a different point of view on the prospects for someone coming up with the new ideas that the field desperately needs. They point out to me that if a really good new idea emerges, string theorists will be glad to work on it, even if it doesn’t involve strings. I point out that this is unlikely to happen unless good young people are encouraged to try new things that don’t fit into the program that string theorists have pursued for the past twenty years. We both then look longingly in Witten’s direction, hoping he’ll come up with something that will save us all, then sigh and say “maybe after 2008 when the LHC results start coming in….”

I must say that I do enjoy reading several of your posts, and in that regard, I like to remind myself: “What does not kill us will make us strong”.

-cvj

Somehow, there, everybody was in a really good mood and the discussion ended up really fruitful.

Well, field theory led us all to believe that the cosmological constant had to be 10^n times larger than it is, didn’t it? So now we *know* that there is something spectacularly wrong about field theory, and that that something is related to cosmology. It’s pretty obvious what one should be thinking about.
Recently I was at a workshop in Canada [not in Toronto..] where somebody suggested that maybe the Universe violates the Null Energy Condition. The response surprised me: basically the participants came down on the hapless questioner like a ton of bricks. No! Impossible! Field theory tells us that that is out of the question! Yeah, just like it told us that the universe should be accelerating 10^n times as fast as it actually does……..

“is it possible that there’s something we’re missing about field theory?”

I’m very glad to see you’re asking that question. It seems to me a crucial one, and following up on it is where hopes for progress lie. One of the main reasons I’ve been on such an anti-string theory campaign is the attitude of string theorists that thinking about field theory is something completely understood, that only fools still think about it, real men do strings, etc…. It seems to me that this attitude has made it very hard for people to work seriously on QFT.

I think you’re exactly right that rigorous field theory isn’t the right thing to think about. There are probably some fundamental missing ideas in our understanding of QFT, and until we have them, we don’t know what the right thing is that we should be trying to make rigorous.

I keep intending to write up my own list of precise things about QFT that seem to me not properly understood, and I wish everyone else in the field would do this. It’s a potentially embarassing thing to do: other people will claim that your problem is that you just don’t understand QFT well enough if you do this.

I’m less happy with your historical analogy. There never was any real problem with mathematical rigor and QM. von Neumann, Weyl and others had no trouble quickly coming up with a rigorous version of QM and proving things about it. The fact that this has been infinitely harder for QFT does make one suspicious that we don’t have the right basic set of ideas.

Back on topic: trying to predict the future is generally not that fruitful, but panel discussions on this topic can be more or less useful depending on the participants, whether they really speak freely, and whether a field is at a point where there are real questions about its future. String theory these days is certainly at such a point. Was this discussion video or audio taped, so we’ll all get to hear what happened?

I certainly can tell that there was a lot of blog reading going on at this conference, my logs are full of connections from utoronto.edu, wireless and others.

Perhaps I’m overly paranoid, but any more I’d rather say in e-mail if anyone cares (and they probably shouldn’t care what I think). One thing I definitely learned from sitting near the back in this conference is that a lot of people read blogs (and newspaper articles about Karl Rove).

On the subject of listening to Joe, his comments involved being puzzled about the nature of dualities, both string theoretical and, more interestingly from my perspective, field theoretical. It brought to mind, for me, the following question. Back when quantum mechanics was young, everyone knew that it made no sense mathematically, but we used it, got the right answers, and nobody cared. A few years later, the mathematicians cleaned it all up, and everyone could be happy. Now we’ve got quantum field theory which makes no sense mathematically, but we get the right answers, and, generally, we don’t care. The thing is, of course, that it’s been quite a while now, and the mathematicians haven’t managed to clean up after us. In fact, from my rather distant perspective, outside of a few theorems, constructive and axiomatic field theory have been spectacularly unfruitful (I’m sure I’ll now get corrected on this point.). So, the question is, is it possible that there’s something we’re missing about field theory? By this, I don’t mean that we should all go out and study rigorous field theory. Rather, I wonder if the fact that nobody’s made it all precise means that there’s something fundamental about the nature of the theory that we just don’t get.

Probably not, but if revolutions tend to come from neglected issues that people generally ignore, that certainly is one. And how, as Joe asked, would one go about proving S-duality in N=4 SYM anyways?

And, lastly, how ’bout a ‘Preview’ button?

Okay, we certainly do a bad job at helping young people decide what to do. I’ve always been (like Clifford, I gather) very much against the two extremist schools of “do what seems popular to enhance your job prospects” and “do just what interests you, regardless of the prospects for further advancement it offers.” Hopefully, there is at least one topic lying in the intersection of what interests you and what interests other people. If not, perhaps you are in the wrong field.

But the panel discussion does address what young people would really want to know — what will be going on in the future, when they are in the thick of things? Sadly, it’s a documented fact that no panel has ever answered this question correctly.

Still, the panels serve a purpose. Get the wise heads up there and let them chatter, without powerpoint slides as crutch. Listen to their less polished thoughts, see what they are interested in. Don’t necessarily believe their predictions — it’s what they don’t say, or are clueless about, that might reveal something important.