SW: Can you explain to us some of the places where supersymmetry shows up in these various theories, and what it does for you when it does show up?
Let me back up for one second here: Supersymmetry is an extension of the symmetries of space-time, and it has this really interesting character. On the one hand, supersymmetric theories are examples of ordinary quantum field theories. They’re not radically outside the framework of the rubric handed down to us by our ancestors by the 1930s. But on the other hand, while being ordinary quantum field theories, they have extraordinary properties; they extend the symmetries of space-time. And so they fit at a nexus between two worlds. Considering this deep, central idea, it’s not surprising that it’s going to show up in a host of places.
One of the places it shows up is in attempts to extend, very pragmatically, the standard model of particle physics and to solve a variety of its problems. So there are these famous fine-tuning problems and other difficulties we have, which can be summarized as attempts to understand the following major puzzle: Because of quantum fluctuations—violent vacuum fluctuations that get more and more violent as you go to shorter and shorter distances—it seems to be impossible to have any macroscopic order in the universe at all. The universe is big, gravity is weak; there is a very big macroscopic universe, but that seems almost impossible given that there are these gigantic quantum fluctuations.
Supersymmetry is one attempt to solve these problems by coming up with an explanation for why the quantum fluctuations disappear at short distances. This isn’t a small problem, a details thing. If you’re going to fix it, it’s going to need a big fix. The way supersymmetry does it is by extending the idea of space-time, and it does it in a way that you can’t fluctuate at all in these quantum dimensions. There’s a perfect symmetry between the quantum dimensions and the ordinary dimensions, and so the gigantic quantum fluctuations have to cancel out. That’s why it showed up and people care about it a lot in particle physics and in finding extensions of the standard model.
It also shows up all over the place in string theory, because if you’re going to have a quantum mechanical theory of gravity, which is what string theory is about, one of the first things it should do is give you a nice big macroscopic universe to play with—even a toy universe. Any other attempt to talk about quantum gravity just fails at this starting point, because of exactly the same violent quantum fluctuation problem. So supersymmetry shows up because it allows us to get going and even talk about it. It also shows up for other reasons.
It turns out that just the structure of quantum field theories—how to calculate with them, and see what the consequences are—is very rich, very complicated, and difficult to calculate with. When the couplings between quarks and gluons get strong, it’s impossible to calculate anything analytically, and for a long time people had no idea how to make progress. Supersymmetric theories have so many theoretical properties that you can really make wonderfully significant progress studying the dynamics of quantum field theories. And you do it by studying them in their most supersymmetric aspect first.
See:Nima Arkani-Hamed on Maximally Supersymmetric Theories– ScienceWatch.com correspondent Gary Taubes.
- An interview with Arkani-Hamed on SUSY by Lubos Motl