Speaker
Description
A Stiefel manifold for $N, p$ integers with $N > p$ is the quotient $\operatorname{SO}(N)/\operatorname{SO}(p)$. In $d = p - 1$ spacetime dimensions (set henceforth $d = 3$), it admits a non-trivial Wess-Zumino--Witten theory. Here, I shall present efforts to study which of these theories admit real fixed points of the renormalisation group flow. I shall work in a Wilsonian implementation, using a weak-coupling expansion for general $N$ and a self-consistent scheme for $N=5$ (the latter based on work with Hawashin-Eichhorn-Janssen-Scherer). It is well known that these theories describe (quasi-)universal properties of exotic phase transitions and phases beyond the Ginzburg--Landau paradigm, with explicit microscopic realisations known at least for $N = 5,6$. For $N > 6$, no known (super-)renormalisable dual Lagrangian is known, rendering them of great intrinsic theoretical interest as well.
