More similar than expected

Some while ago I have written about a project a master student and myself have embarked upon: Using a so-called supersymmetric theory - or SUSY theory for short - to better understand ordinary theories.

Well, this work has come to fruition, both in the form of the completion of the master project as well as new insights written up in a paper. This time I would like to present these results a little bit.

To start, let me briefly rehearse what we did, and why. One of the aims of our research is to better understand how the theories work we are using to describe nature. A particular feature of these theories is redundancy. This redundancy makes many calculations possible, but at the same time introduces new problems, mainly about how to get unique results.

Now, in theories like the standard model, we have all problems at the same time: All the physics, all the formalism, and especially all the redundancy. But this is a tedious mess. It is therefore best to reduce the complexity and solve one problem at a time. This is done by taking a simpler theory, which has only one of the problems. This is what we did.

We took a (maximal) SUSY theory. In such a theory, the supersymmetry is very constraining, and a lot of features are exactly known. But the implications of redundancy are not. So we hoped that by applying the same procedures we use to deal with the redundancy in ordinary theories to this theory, we could check whether our approach is valid.

Of course, the first, and expected, finding was that even a very constraining theory is not simple. When it comes to technical details, anything interesting becomes a hard problem. So it required a lot of grinding work before we got results. I will not bore you with the details. If you want them, you can find them in the paper. No, here I want to discuss the final result.

The first finding was a rather comforting one. Doing the same things to this theory that we do to ordinary theories did not do too much damage. Using these approximations, the final results were still in agreement with what we do know exactly about this theory. This was a relief, because this lends a tiny amount of support more to what we are usually doing.

The real surprise was, however, a very different one. We knew that this theory shows a very different kind of behavior than all the theories we are usually dealing with. So we did expect that, even if our methods work, the results will still be drastically different from the other cases we are dealing with. But this was not so.

To understand better what we have found, it is necessary to know that this theory is similar in structure to a conventional theory. This conventional one is a theory of gluons, but without quarks to make the strong interactions complete. In the SUSY theory, we also have gluons. In addition, we have further new particles, which are needed to get.

The first surprise was that the gluons behaved unexpectedly similar to their counterparts in the original theory. Of course, there are differences, but these differences were expected. They came from the differences of both theories. But where they could be similar, they were. And not roughly so, but surprisingly precisely so. We have an idea why this could be the case, because there is one structural property, which is very restricting, and which appears in both theories. But we know that this is not enough, as we now other theories where this still is different, despite also having this one constraining structure. Since the way how the gluons are very similar is strongly influenced by the redundancy features of both theories, we can hope that this means we are treating the redundancy in a reasonable way.

The second surprise was that the new particles mirror the behavior of the gluons. Even though these particles are connected by supersymmetry to the gluons, the connection would have allowed many possible shapes of relations. But no, the relation is an almost exact mirror. And this time, there is no constraining structure which gives us a clue why, out of all possible relations, this one is picked. However, this is again related to redundancy, and perhaps, just speculating here, this could indicate more about how this redundancy works.

In total, we have learned quite a lot. We have more support for what we doing in ordinary theories. We have seen that some structures might be more universal than expected. And we may even have a clue in which direction we could learn more about how to deal with the redundancy in more immediately relevant theories.