Higher spin gauge theory and holography: the three-point functions

Abstract

In this paper we calculate the tree level three-point functi ons of Vasiliev’s higher spin gauge theory in AdS 4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the fre e field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.