In a few weeks, I’ll be giving a talk for Stony Brook’s Graduate Awards Colloquium, to an audience of social science grad students and their parents.
One of the most useful tools when talking to people in other fields is a shared image. You want something from your field that they’ve seen, that they’re used to, that they’ll recognize. Building off of that kind of thing can be a great way to communicate.
If there’s one particle physics image that lots and lots of people have seen, it’s the Standard Model. Generally, it’s organized into charts like this:
I thought that if people saw a chart like that, but for N=4 super Yang-Mills, it might make the theory seem a bit more familiar. N=4 super Yang-Mills has a particle much like the Standard Model’s gluon with spin 1, paired with four gluinos, particles that are sort of but not really like quarks with spin 1/2, and six scalars, particles whose closest analogue in the Standard Model is the Higgs with spin 0.
In N=4 super Yang-Mills, none of these particles have any mass, since if supersymmetry isn’t “broken” all particles have the same mass. So where mass is written in the Standard Model table, I can just put zero. The table I linked also gives the electric charge of each particle. That doesn’t really mean anything for N=4 super Yang-Mills. It isn’t a theory that tries to describe the real world, so there’s no direct equivalent to a real-world force like electromagnetism. Since everything in the theory has to have the same charge, again due to supersymmetry, I can just list all of their “electric charges” as zero.
Putting it all together, I get the diagram below. The theory has eleven particles in total, so it won’t fit into a nice neat square. Still, this should be more familiar than most of the ways I could present things.