Interactions in higher-spin gravity: A holographic perspective

This review is an elaboration of recent results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured duality with free conformal field theories (CFTs). After reviewing the general approach and establishing the necessary intermediate results, we extract explicit expressions for the complete cubic action on ${\rm AdS}_{d+1}$ and the quartic self-interaction of the scalar on AdS4 for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar $O(N)$ vector model. For this purpose tools were developed to evaluate tree-level three-point Witten diagrams involving totally symmetric fields of arbitrary integer spin and mass, and the conformal partial wave expansions of their tree-level four-point Witten diagrams. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.