Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings

In this Letter we provide a complete holographic reconstruction of the cubic couplings in the minimal bosonic higher spin theory in (d + 1)-dimensional anti- de Sitter space. For this purpose, we also determine the operator-product expansion coefficients of all single-trace conserved currents in the d-dimensional free scalar O(N) vector model, and we compute the tree-level three-point Witten diagram amplitudes for a generic cubic interaction of higher spin gauge fields in the metriclike formulation.