Higher-spin Interactions from CFT: The Complete Cubic Couplings

TL;DR

This paper reconstructs the complete set of cubic interactions in higher-spin theories in AdS space by analyzing OPE coefficients and computing three-point amplitudes in a holographic framework.

Contribution

It provides the first full holographic reconstruction of all cubic couplings in minimal bosonic higher-spin theory in AdS, linking CFT data with bulk interactions.

Findings

Determined OPE coefficients for all conserved currents in free scalar O(N) model.

Computed tree-level three-point Witten diagrams for higher-spin interactions.

Established a complete correspondence between CFT data and bulk cubic couplings.

Abstract

In this letter we provide a complete holographic reconstruction of the cubic couplings in the minimal bosonic higher-spin theory in AdS$_{d+1}$. For this purpose we also determine the OPE coefficients of all single-trace conserved currents in the $d$-dimensional free scalar $O\left(N\right)$ vector model, and compute the tree-level three-point Witten diagram amplitudes for a generic cubic interaction of higher-spin gauge fields in the metric-like formulation.