August 09, 2004

Returned from Colorado; Thinking about supersymmetry

Posted by Matt

I'm back from Colorado (I've been in Louisville for about a week, for that matter). A small fraction of the pictures from the trip are here. The weather was cooler and rainier than usual, which is probably correlated with how much more active the wildlife seemed to be. (The foxes were brave or foolish enough to walk within a few feet of us, hence the very good pictures of them.) We did a lot of hiking. If you're ever in Rocky Mountain National Park and only have a day or so (and the altitude doesn't bother you too much), I suggest taking the hike starting from Bear Lake, and progressing down to Odessa and Fern Lakes. It's about 9 miles, if I remember correctly, but all the uphill part is at the beginning. There are spectacular views of the mountains, and beautiful lakes and streams.

In the time since I last posted I've read a number of novels, and watched a handful of movies, so later I might post some selected commentary on those. I've also been working on learning some physics, about which I'll elaborate in this post. Read on for some thoughts on supersymmetry, and why it's important to study it whether or not our world is supersymmetric at experimentally accessible energies.

Back in April I wrote this post summarizing the forces we see in nature (gravity, electromagnetism, the weak force, and the strong force). I mentioned there that two of these are part of a unified "electroweak" interaction, characterized by certain symmetries that are only manifest at high energies. How these symmetries are "broken" to give the two distinct forces we see at low energies is still an open question experimentally, but one that we hope will be answered by the Large Hadron Collider at CERN in a few years.

The simplest possibility is that there is a particle called the Higgs boson, that is responsible for the symmetry breaking. (See this Wikipedia article for some details.) This is the "easy," naive answer to what you can do to the theory mathematically to produce what we see in nature. But the theory with the Higgs has its own problems; to make sense, certain parameters of the theory have to be "fine-tuned" to very high accuracy, or the predictions are nonsensical. We generally don't like fine-tuning in physics, preferring to have answers that are dynamically chosen. (We don't like having to believe that things just accidentally worked out in the right way, which leads some to invoke the anthropic principle.)

The effects that lead to this need for fine-tuning are all "quantum corrections" to the simple classical Higgs theory. One possibility for building a better theory that isn't spoiled by these corrections is to invoke new symmetry, called supersymmetry, positing that every boson has a fermion partner and vice versa. Bosons and fermions give quantum corrections with opposite signs, nicely cancelling, and eliminating the need for fine-tuning. There are problems with this idea, though. None of the known bosons and fermions can be paired under supersymmetry, so this makes the drastic prediction that there are many particles we have not discovered. It also predicts that all the partners should have the same mass, which is demonstrably not true in our world. So, if supersymmetry is a property of nature, it is broken. Explaining how it is broken is a big problem on the order of our original problem of explaining how electroweak symmetry is broken, so you might wonder why we would take this theory seriously. (After all, it seems to blatantly go against Ockham's razor.)

One answer is that we can construct plausible models with broken symmetry that look like the real world, and might explain other phenomena like dark matter in the process. If these models are true people expect we'll see experimental evidence at the LHC.

That's the familiar answer, and I'd like to supply a different one. The outline I'm about to give is fairly well-known, but it's not something you hear as often as the above "supersymmetry fixes the Higgs" sort of argument.

Supersymmetry puts strong constraints on theories. This makes it possible to calculate things that you just aren't capable of understanding in non-supersymmetric theories. In fact, this might give us a way to understand a fundamentally different type of electroweak symmetry breaking from the simple Higgs models. It's fairly well-known (though I'm not sure I could give a detailed argument) that aside from having a Higgs sector, the only other way to break electroweak symmetry is to have some sort of new strongly interacting physics at around the TeV scale. This means having a new gauge symmetry where the gauge bosons interact in a way similar to the way the gluons of QCD interact. The original ideas along these lines were called "technicolor," and have been experimentally ruled out.

However, we don't really know much at all about strongly interacting gauge theories. We observe the strong force of QCD, but a lot of what we know about it comes from high-energy experiments, and at high energies where you probe individual quarks, the strong force isn't really so strong anymore. We can calculate in that regime; the calculational techniques of particle physics involve taking the first few terms of a series where each successive term is multiplied by a "coupling constant" indicative of how strong an interaction is. When the coupling constant is small, these successive terms get smaller, and you can approximate an answer by just a couple of terms. Such a calculation is called "perturbative." When the coupling constant is large, this no longer makes any sense. Thus, QCD at low energies is nonperturbative, and our main calculational tool is to use computers to do something called "lattice QCD."

Since calculations are hard to do in strongly interacting theories, and we only have experimental access to one such theory so far (QCD), it's hard to have a good sense of the different ways such theories can behave. Simple QCD-like technicolor models might be ruled out, but what if there's some other sort of strongly interacting physics responsible for electroweak symmetry breaking? We could see it at the LHC and not really know what we're looking at. It's important, then, to try to better understand the possible types of strongly interacting physics within the next few years, before the LHC turns on.

This is where supersymmetry can be useful. Having this powerful symmetry greatly constrains nonperturbative properties of the theory. In short, it makes it possible to calculate things that we just can't calculate in nonsupersymmetric theories. These methods were pioneered by Nathan Seiberg and others in the early-to-mid 1990s, and progress continues to be made today. (Csaba Csaki at Cornell has done some work on a new idea of Intriligator and Wecht called "a-maximization" for looking at such theories, which is one of the reasons I've been trying to catch up on all these things.)

In short, the hope is that understanding in detail the physics of highly constrained supersymmetric field theories will give us a better understanding of the possible behavior of strongly interacting physics in general. Then, whether supersymmetry is present in the real world at accessible energies or not, the things we learn from these theories can be powerful guides. In a few years we might be facing experimental evidence of some phase of strongly interacting gauge theory that we have never seen before, and the only way to understand electroweak symmetry breaking might be to identify the experimental signatures of this new strong interaction. Then, the seemingly abstract work of Seiberg and others might start telling us a great deal about the world around us.

If you know some field theory and want to learn about supersymmetric field theories, I'd suggest working through Lykken's lecture notes, then moving on to those by Peskin and Terning.

Also of note: the KITP at Santa Barbara is having a program on "QCD and Strings," looking at how string theory might shed light on QCD. The first lecture, by Matt Strassler, is online now and well worth watching. (Especially to hear him emphatically claim that he never does supergravity. Trust me, watch to the end, it gets exciting.)

Posted by Matt at August 9, 2004 12:26 AM

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