Description
Higher spin gravity theories in Anti-de Sitter space have
been conjectured to be holographically dual to conformal
field theories with vector-like matter fields: these include
the free CFT's of N-component massless scalars or fermions,
but also interacting CFT's such as the Wilson-Fisher fixed
point in d=3. I will review recent tests of these dualities
in various spacetime dimensions, and also discuss evidence
for the existence of non-trivial large N scalar CFT's with
O(N) symmetry in 4<d<6.
