Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory

TL;DR

This paper derives all correlation functions of conserved currents in a conformal field theory dual to unbroken Vasiliev higher-spin theory, emphasizing symmetry invariance and algebraic structures without boundary limits or bulk integrals.

Contribution

It provides a complete algebraic construction of all correlators in the dual CFT using higher-spin symmetry, linking boundary algebraic structures to bulk theory.

Findings

All correlators are expressed as invariants of higher-spin symmetry.

Boundary-to-bulk propagators form an algebraic structure at the boundary.

N-point functions are represented as products of algebraic elements.

Abstract

All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), semidirect product of Sp(4) and the Heisenberg group. N-point correlation function is given by a product of N elements.