**Higher spin theories, holography and Chern-Simons vector models**

Abstract:

I will first briefly overview recent progress in testing the
holographic duality between
3d vector models and higher spin gravity theories in four-dimensional
Anti-de Sitter space.
I will then discuss some new results on the CFT obtained by coupling
3d vector models
to a Chern-Simons gauge field. In particular, I will show that such
theory has a higher spin
symmetry in the infinite N limit, and propose that it should be
holographically dual
to a parity breaking higher spin gravity theory.