A Note on (Non)-Locality in Holographic Higher Spin Theories

Abstract

It was argued recently that the holographic higher spin theory features non-local interactions. We further elaborate on these results using the Mellin representation. The main difficulty previously encountered on this way is that the Mellin amplitude for the free theory correlator is ill-defined. To resolve this problem, instead of literally applying the standard definition, we propose to define this amplitude by linearity using decompositions, where each term has the associated Mellin amplitude well-defined. Up to a sign, the resulting amplitude is equal to the Mellin amplitude for the singular part of the quartic vertex in the bulk theory and, hence, can be used to analyze bulk locality. From this analysis we find that the scalar quartic self-interaction vertex in the holographic higher spin theory has a singularity of a special form, which can be distinguished from generic bulk exchanges. We briefly discuss the physical interpretation of such singularities and their relation to the Noether procedure.

arXiv comment22 pages, 2 images; additional clarifications on the proposal for the Mellin amplitude and its connection to the literature given

References in corpus (32)

• AdS Dual of the Critical O(N) Vector Model
• Holography from Conformal Field Theory
• Massless Higher Spins and Holography
• Writing CFT correlation functions as AdS scattering amplitudes
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• OPE Convergence in Conformal Field Theory
• A Natural Language for AdS/CFT Correlators
• Emergent Spacetime and Holographic CFTs
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• How to Succeed at Holographic Correlators Without Really Trying
• Conformal Bootstrap in Mellin Space
• Light-Front Higher-Spin Theories in Flat Space
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Scattering in Anti-de Sitter Space and Operator Product Expansion
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Chiral Higher Spin Theories and Self-Duality
• Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex
• On four-point interactions in massless higher spin theory in flat space
• Mellin Amplitudes for Dual Conformal Integrals
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Higher-Spin Algebras, Holography and Flat Space
• On triviality of S-matrix in conformal higher spin theory
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Star Integrals, Convolutions and Simplices
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Scalar scattering via conformal higher spin exchange
• Bulk quartic vertices from boundary four-point correlators
• Pseudo-local Theories: A Functional Class Proposal
• A note on the analyticity of AdS scalar exchange graphs in the crossed channel
• Exploring Perturbative Conformal Field Theory in Mellin space

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• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
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• Vertex-Constraints in 3D Higher Spin Theories
• Chiral Higher Spin Gravity and Convex Geometry
• On one loop corrections in higher spin gravity
• A Stringy theory in three dimensions and Massive Higher Spins
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• Character Integral Representation of Zeta function in AdS${}_{d+1}$: II. Application to partially-massless higher-spin gravities
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
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• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• On gauge-invariant deformation of reducible gauge theories
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories