Yesterday I spent the day at Stony Brook, one of the branches of the State University of New York (SUNY), which has a long and distinguished history, and a bright future, in high-energy physics and related fields. It is the home of the C.N.Yang Institute and the Simons Center. My main task was to deliver a colloquium on the Large Hadron Collider [LHC] (roughly the same talk I gave at Harvard recently) but the real pleasure of the visit (at least for me) was catching up with what some of my colleagues who work there, or who were themselves visiting there, have been doing recently.
One thing I’ve not talked about yet on this website — mainly because it is more technical than LHC physics — is that a lot of progress is being made right now understanding the fundamentals of my entire research area. I refer here to what is known as “quantum field theory” [QFT for short]. It’s not a “theory” in the colloquial sense of “hunch” or “conjecture”, where you imagine someone saying “my theory is that it was the butler’s fault”. This is a second meaning, very common in science, of the word “theory”: a mathematical framework for scientific calculations, and a conceptual framework that goes along with it.
Quoting from my Higgs FAQ, a field is something that
- is present everywhere in space and time,
- can be, on average, zero or not zero, and
- can have waves in it.
- And if it is a quantum field, its waves are made from particles.
One example of a field is the wind. Another is the electric field. A third is the Higgs field. And there are many more. In particular, every type of elementary particle is a ripple in a corresponding quantum field. [There’s a bit on this in the video clips from a recent public talk that I gave at the Secret Science Club.]
The general class of equations that we use to calculate the behavior of quantum fields — quantum field theory — is therefore crucial in particle physics. In fact, you can’t do much particle physics or string theory without running into the mathematics of QFT. The subject also has a big role to play in cosmology (the history of the universe) and in the research area known as “condensed matter physics”, which includes as a big subset the physics of solid materials.
Although quantum field theory was invented in the middle of last century, it still holds many great mysteries, and there’s still an enormous amount for us to learn. I myself have spent much of my career studying new methods for understanding the behavior of and making predictions in quantum field theory. And though right now my focus is on the LHC, I’ve been fascinated by several recent important developments in the subject, including advances in answering decades-old questions.
My day at Stony Brook was mostly filled with discussions of these issues… the most striking being a fairly convincing proof, by Zohar Komargodski and Adam Schwimmer, of a 30-year old conjecture (due to John Cardy, I believe) of what is known as the “a-theorem”. Roughly speaking, a quantum field theory in a world like ours, with three spatial dimensions and one time dimension, has a calculable quantity, called “a” for historical reasons, that helps characterize it. The conjecture is that if you take any quantum field theory, and study the phenomena that it exhibits at longer and longer distance (for instance, if you compare how a quark and an antiquark behave when they are very close together to how they behave when they are further apart) you will find that “a” always decreases. [Very roughly: at short distances quarks and antiquarks can bounce off each other easily, through the strong nuclear force, but at long distances the strong nuclear force traps them tightly inside hadrons, such as a proton. In this transition, the quantity “a” decreases.] There’s been lots of evidence in favor of this conjecture for many years, but now a proof seems to have been found — and what is nice is that it requires a tricky and interesting new technical idea, after which the proof becomes elegant and simple.
15 thoughts on “A Day At Stony Brook”
Hi Matt (?…) :-),
know You have made me very curious about what this “a” You write about in the last section is …
I first thought it is something like a coupling constant.
Does this decreasing “a” help to go “smoothly” from physics around the Planck scale to effective QFTs such as the standard model?
I apologize if I´m completely off base… For me this last section sounds very interesting but it is written too general and with too little details to guess what it really means …
I apologize if I´m completely off base, I`d just like to read more …
Prof. Matt Strassler,
Look forward to the explanation of the proof.
For a long time now I have been interested in “a” emergent product from a condensed matter theorist point of view( these have been extolled from Witten and others for along time). If it can be mathematically satisfying, then it must “on another level” play a part in the description of the expression of the what happens in the universe?” Especially, when revealed as a expression in the symmetry breaking, as if a false vacuum to the true.
It is asymmetrically pleasing then, that any foundation could have such a basis as if we would approach it from dimension attribution and geometrical correspondences?
Yes, I think the idea of an a-theorem goes back to Cardy, building on the earlier result of Zamolodchikov. See J. Cardy (1988), “Is there a c-theorem in four dimensions?” Physics Letters B 215, 4: 749–52.
Having a proof of the a-theorem is very exciting, especially given some proposed counter-examples (which were later clarified). I just thought that your description of the quark-antiquark pair may be misleading, or maybe I am the one who is confused. Since QCD is confining, separating a qqbar pair by large distances leads to higher energies and so it is not clear to me that the separation is going to correspond to RG scale. Of course, you didn’t say that the two were bound together or that they were the only particles around, etc.
Are there compelling conjectures for what plays the role of “c” or “a” in other dimensions or even in general (the paper mentions 3 and 6)?
Steve — you are sort of right, but not entirely, I think… after all (as I emphasized in my jets article) when you separate a q qbar pair by a large distance, what actually happens in QCD is that the string that tries to form breaks, and you end up with two pions… which are quite light and at low energy. [The more technical way to say this would have been to use a Wilson loop; since there is always a perimeter law, and in one limit you have gluon exchange and in the other pion or sigma exchange, I think the ground I’m on, though a bit shaky, isn’t quicksand.] Of course that would not be true if there were no lightweight quarks in nature: but if there were no lightweight quarks, then indeed I would have used a different example.
What I was really trying to do here was not make a technically precise statement, but one which would allow a non-expert to understand what asking questions at short and long distances would mean. If I wanted to make a technically precise statement, I would have taken some of the quarks to be massless, so that the theory would have strictly massless pions; and then everything I said would have been precisely correct, with “a” easily computable both at very short and very long distances.
About other dimensions: Komargodski clearly has some ideas (and I guess some other people do too), but I do not want to repeat unpublished ideas in a public forum. You might look at recent work by Myers and Sinha, but that may be what you already saw referenced in the Komargodski-Schwimmer paper. I’m sure we will see many interesting papers on this subject.
Prof.Matt Strassler: “What I was really trying to do here was not make a technically precise statement, but one which would allow a non-expert to understand what asking questions at short and long distances would mean.”
As a layman while seeing the “strength and weakness of the tension in that QQ distance” what other way may one see this example other then in what one may find in definition regarding Quark Confinement or Bag Model- http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qbag.html#c1
Regarding a stringy theory model apprehension it occurred to me that such distinction would have been more then about colliding billiard balls on a table, but also, about the sound they are making as they connect.
So I see the QFT in that context. Is that wrong?
A related question: do “bare” particles exist? Those non-interacting (bare) particles whose interactions result in real particles. 😉
If you can’t measure it, even in principle, it probably doesn’t make sense to say it exists. Experience has shown that if you try to make sense of things that you can’t measure, and you try to calculate their properties, the result is (a) infinity, or (b) ambiguous, or (c) nonsensical. The fantastic thing about quantum field theory is that it gives sensible answers for all physically-meaningful questions, even though it gives insane answers for lots of other questions you might try to ask. There are infinities, ambiguities, and bizarre behaviors all over the place — but when you ask a good question, you get a good answer.
Yes, one can “extract” the right result, especially if one knows it in advance. I, however, do not think it is fantastic. I designed a simple demonstration of how we make mistake while coupling and how we get the right result due to renormalizaton. http://arxiv.org/abs/1110.3702 Enjoy!
I look to know and incorporate this knowledge into my art. Thank you.
Stony Brook as a location for a university is kind of the worst of both worlds. It’s not New York City, but it’s close enough to a huge population of people who already have lives close by, and aren’t that interested in starting a new life in Stony Brook. If we were in New York City, we’d still have a lot of people from close by, but people would want to stay in the city, because… well it’s the city. If we were upstate, almost everyone would be cut off from their old lives and would actually be making a new life at Stony Brook.
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