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.