Physical examples of Bott periodicity

Question

Are there any interesting families of theories in all dimensions with 8 periodic behavior in the dimension?

Comments

What exactly is 8 periodic behavior or Botts periodicity?

---

Oh man, this is some seriously beautiful stuff which reaches incredibly deep into mathematics. I especially enjoy John Baez' expositions on the subject: http://math.ucr.edu/home/baez/week105.html (and the next week) http://math.ucr.edu/home/baez/week195.html . You're in for a crazy ride!

---

Thanks Ryan, I will look into it to fill my present gap of ignorance :-)

Answer 1

I've only known the subject very superficially, but I think Bott periodicity appears in the classification of topological insulators in all spatial dimensions, for example the Kitaev's classification scheme. Here's a SE post explaining the physical relevance of such classification scheme.

Answer 2

The simplest 8 periodicity related to Bott periodicity and of every day use in physics is the one of the representation theory of the Spin groups.

What is generally called precisely Bott periodicity is about topological K-theory. Topological K-theory is where the charges of D-branes in string theory live. In particular, Bott periodicity has consequences for D-branes. The most obvious one comes from the "complex" Bott periodicity, which is a 2 periodicity and related to the alternance of even-odd dimensions for D-branes in Type IIA-IIB. It is also possible to see the more complicated 8-periodicity i.e. "real" Bott periodicity in the structure of D-branes in Type I. See for example http://arxiv.org/abs/hep-th/9810188