Interactions in Higher-Spin Gravity: a Holographic Perspective

Abstract

This thesis 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 holographic 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 AdS$_{d+1}$ and the quartic self-interaction of the scalar on AdS$_4$ 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 $O\left(N\right)$ vector model. For this purpose tools were developed to evaluate tree-level three-point Witten diagrams involving fields of arbitrary integer spin and the conformal partial wave expansions of tree-level four-point Witten diagrams, which are underpinned by the ambient space formulation of AdS space and CFT. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.