Appropriate for Advanced Non-Experts
[This is the seventh post in a series that begins here.]
In the last post in this series, I pointed out that there’s a lot about quantum field theory [the general case] that we don’t understand. In particular there are many specific quantum field theories whose behavior we cannot calculate, and others whose existence we’re only partly sure of, since we can’t even write down equations for them. And I concluded with the remark that part of the reason we know about this last case is due to “supersymmetry”.
What’s the role of supersymmetry here? Most of the time you read about supersymmetry in the press, and on this website, it’s about the possible role of supersymmetry in addressing the naturalness problem of the Standard Model [which overlaps with and is almost identical to the hierarchy problem.] But actually (and I speak from personal experience here) one of the most powerful uses of supersymmetry has nothing to do with the naturalness problem at all.
The point is that quantum field theories that have supersymmetry are mathematically simpler than those that don’t. For certain physical questions — not all questions, by any means, but for some of the most interesting ones — it is sometimes possible to solve their equations exactly. And this makes it possible to learn far more about these quantum field theories than about their non-supersymmetric cousins.
Who cares? you might ask. Since supersymmetry isn’t part of the real world in our experiments, it seems of no use to study supersymmetric quantum field theories.
But that view would be deeply naive. It’s naive for three reasons.