Can We Understand the Standard Model Using Octonions?



I gave two talks in Latham Boyle and Kirill Krasnov’s Perimeter Institute workshop Octonions and the Standard Model.

The first talk was on Monday April 5th at noon Eastern Time. The second was exactly one week later, on Monday April 12th at noon Eastern Time.

Here they are:

Can we understand the Standard Model? (video, slides)

Abstract. 40 years trying to go beyond the Standard Model hasn’t yet led to any clear success. As an alternative, we could try to understand why the Standard Model is the way it is. In this talk we review some lessons from grand unified theories and also from recent work using the octonions. The gauge group of the Standard Model and its representation on one generation of fermions arises naturally from a process that involves splitting 10d Euclidean space into 4+6 dimensions, but also from a process that involves splitting 10d Minkowski spacetime into 4d Minkowski space and 6 spacelike dimensions. We explain both these approaches, and how to reconcile them.

The second is on Monday April 12th at noon Eastern Time:

Can we understand the Standard Model using octonions? (video, slides)

Abstract. Dubois-Violette and Todorov have shown that the Standard Model gauge group can be constructed using the exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices of octonions. After an introduction to the physics of Jordan algebras, we ponder the meaning of their construction. For example, it implies that the Standard Model gauge group consists of the symmetries of an octonionic qutrit that restrict to symmetries of an octonionic qubit and preserve all the structure arising from a choice of unit imaginary octonion. It also sheds light on why the Standard Model gauge group acts on 10d Euclidean space, or Minkowski spacetime, while preserving a 4+6 splitting.

You can see all the slides and videos and also some articles with more details here.

5 Responses to Can We Understand the Standard Model Using Octonions?

  1. I tried to register, but it rejects my various email addresses as invalid. Maybe it thinks that only those which end in .edu are “valid”. :-(

  2. Wyrd Smythe says:

    I was fascinated by Cohl Furey’s YouTube lectures on octonions and the standard model. Although a great deal of it was over my head (I’m still chewing on quaternions, and Clifford algebras are foreign territory to me), the stuff that wasn’t seemed to make a lot of sense. At the time it seemed very speculative, but maybe the idea is taking hold?

    • John Baez says:

      It depends a lot on what you mean by “the idea”. Cohl Furey and Mia Hughes have some ideas involving the Standard Model and octonions, Kirill Krasnov has some others, Latham Boyle has some others and Dubois-Violette and Todorov have some others!

      My talks only describe some mathematical facts connecting octonions and the Standard Model—I’m not proposing a theory. The most exciting of these facts was first discovered by Dubois-Violette and Todorov, and my second talk explains it.

  3. John Baez says:

    I massively revised my second deck of slides:

    Can we understand the Standard Model using octonions?

    I now give a rough explanation of why the subgroups

    (\mathrm{SU}(3) \times \mathrm{SU}(3))/\mathbb{Z}_2,  \; \mathrm{Spin}(9) \subset \mathrm{F}_4

    show up in this game, and why their intersection is the true gauge group of the Standard Model.

  4. Keith Harbaugh says:

    PI has quite a lot at YT, as can be seen by visiting YT and searching on “Perimeter Institute”, but I could not find these lectures.

    These are top-secret lectures for experts only.

    Just kidding! How many of the Perimeter Institute Recorded Seminar Archive lectures are on YouTube, anyway?

    I don’t really care if these lectures of mine are on YouTube except that it might slightly increase the chance of their being preserved for a long time. I downloaded copies for that reason.

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