Lifting a Conformal Field Theory from D-Dimensional Flat Space to (D+1)-Dimensional Ads Space

Abstract

A quantum field theory on Anti-de-Sitter space can be constructed from a conformal field theory on its boundary Minkowski space by an inversion of the holographic mapping. To do this the conformal field theory must satisfy certain constraints. The structure of operator product expansions is carried over to AdS space. We show that this method yields a higher spin field theory HS(4) from the minimal conformal O(N) sigma model in three dimensions. For these models AdS/CFT correspondence is hereby proved to second order in the coupling constant.

Latex file, 19 pages; one section added, 3 references added, typos corrected

References in corpus (2)

• The masses of gauge fields in higher spin field theory on AdS(4)
• Coupling of Higher Spin Gauge Fields to a Scalar Field in $Ad{S}_{d+1}$ and their Holographic Images in the $d$-Dimensional Sigma Model

Cited by in corpus (11)

• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• The masses of gauge fields in higher spin field theory on AdS(4)
• Intertwining Operator Realization of anti de Sitter Holography
• The off-shell behaviour of propagators and the Goldstone field in higher spin gauge theory on $Ad{S}_{d+1}$ space
• The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $Ad{S}_4$
• The structure of the trace anomaly of higher spin conformal currents in the bulk of $Ad{S}_4$
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
• Protecting the conformal symmetry via bulk renormalization on Anti deSitter space
• Towards a quantum field theory of primitive string fields