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

V. E. Didenko, E. D. Skvortsov

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.

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

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.

Paper Structure

This paper contains 22 sections, 94 equations, 1 figure.

Table of Contents

  1. Introduction
  2. HS prerequisites
  3. Higher-spin algebra.
  4. Linearized equations.
  5. Reality conditions.
  6. Symmetries and general solution.
  7. Boundary-to-bulk propagators
  8. Background in Poincare coordinates.
  9. Bulk-to-boundary propagators.
  10. Invariant properties of propagators.
  11. Interplay between bulk and boundary global symmetries.
  12. Observables in higher-spin theory
  13. General expression.
  14. Algebraic structure of propagators
  15. $\boldsymbol{Sp(2M)\ltimes}$Heisenberg group and Cayley transform.
  16. ...and 7 more sections

Figures (1)

  • Figure 1: Twistor space Witten diagram for $O_n$