### Revisiting the epsilon expansion

There are many interacting CFTs with scalar degrees of freedom, like the O(N) fixed point in 2 < d < 4 dimensions. Surprisingly, little is known about the classification of such fixed points, even in perturbation theory. In this talk I will explore this well-known problem in the framework of the epsilon expansion. I will argue that consistent CFTs can only live in a small region of the high-dimensional space of all possible theories, and I'll discuss bounds on spectra of anomalous dimensions. Finally I’ll address the same question in the case of N gauged complex scalars, which leads to qualitatively different answers.

**Tuesday, 18th of February 2019, 14:30, sala Wataghin**