Interactions in Higher-Spin Gravity: a Holographic Perspective

Abstract

This thesis is an elaboration of recent results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured holographic duality with free conformal field theories (CFTs). After reviewing the general approach and establishing the necessary intermediate results, we extract explicit expressions for the complete cubic action on AdS${}_{d+1}$ and the quartic self-interaction of the scalar on AdS${}_4$ for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar $O\left(N\right)$ vector model. For this purpose tools were developed to evaluate tree-level three-point Witten diagrams involving fields of arbitrary integer spin and the conformal partial wave expansions of tree-level four-point Witten diagrams, which are underpinned by the ambient space formulation of AdS space and CFT. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.

Ph.D. thesis, 246 pages, 14 figures. Advisor: Prof. Dr. Johanna Erdmenger. v2: Minor edits, refs added and typos fixed. Published as a topical review in Journal of Physics A

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• Writing CFT correlation functions as AdS scattering amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• Spinning AdS Propagators
• Higher Spins & Strings
• Light-Front Higher-Spin Theories in Flat Space
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• Higher-Spin Algebras, Holography and Flat Space
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Cited by in corpus (26)

• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• On the Inflationary Perturbations of Massive Higher-Spin Fields
• Spinning Witten Diagrams
• Spinning AdS Loop Diagrams: Two Point Functions
• Momentum space approach to crossing symmetric CFT correlators
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Anatomy of Geodesic Witten Diagrams
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space
• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• Basic introduction to higher-spin theories
• Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Lectures on Higher Spin Holography
• Bootstrapping Witten diagrams via differential representation in Mellin space
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Superconformal Block from Holographic Geometry
• Holographic coordinates
• On Gluing CFT Correlators to Higher-Spin Amplitudes in AdS
• The higher spin Laplace operator in several vector variables