On Higher Spin Gauge Theory and the Critical O(N) Model

We show that the differences between correlators of the critical O(N) vector model in three dimensions and those of the free theory are precisely accounted for by the change of boundary condition on the bulk scalar of the dual higher spin gauge theory in AdS4. Thus, the conjectured duality between Vasiliev's theory and the critical O(N) model follows, order by order in 1/N, from the duality with free field theory on the boundary.