Cubic interactions of massless higher spins in (A)dS: metric-like approach

TL;DR

The paper addresses the long-standing problem of constructing consistent cubic interactions for bosonic symmetric higher-spin fields in (A)dS. It develops a metric-like, transverse-traceless framework complemented by an ambient-space formalism to relate (A)dS cubic vertices to flat-space structures, enabling a complete, parity-invariant classification for $d>=4$. The authors derive a closed-form construction of all TT-consistent cubic vertices in $(A)dS_d$, organized as a flat-space–guided series with controlled expansions in the cosmological constant $Λ$, and show how these ambient-space vertices reduce to intrinsic (A)dS expressions. This work clarifies the Fradkin–Vasiliev vertex structure, connects with the BLS limit, and sets the stage for higher-order interactions and holographic applications in AdS/CFT.

Abstract

Cubic interactions of higher-spin gauge fields in (A)dS are studied in the metric-like approach. Making use of the traceless and transverse constraints together with the ambient-space formalism, all consistent parity-invariant cubic vertices are obtained for d>3 in closed form pointing out the key role of their flat-space counterparts.