On one loop corrections in higher spin gravity

Abstract

We propose an approach to compute one-loop corrections to the four-point amplitude in the higher spin gravities that are holographically dual to free $O(N)$, $U(N)$ and $USp(N)$ vector models. We compute the double-particle cut of one-loop diagrams by expressing them in terms of tree level four-point amplitudes. We then discuss how the remaining contributions to the complete one-loop diagram can be computed. With certain assumptions we find nontrivial evidence for the shift in the identification of the bulk coupling constant and $1/N$ in accordance with the previously established result for the vacuum energy.

25 pages, several figures; few comments added, the discussion of the incompleteness of Vasiliev equations reduced; replaced with the published version

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• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Higher Spin Gravities and Presymplectic AKSZ Models
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• On interacting quantum fields in various charts of anti de Sitter space-time
• Unfolded Dynamics Approach and Quantum Field Theory
• A calculation of the Weyl anomaly for 6D Conformal Higher Spins
• Dressing in AdS and a Conformal Bethe-Salpeter Equation