A String Model for AdS Gravity and Higher Spins

Abstract

We construct a string sigma-model which low energy limit describes the anti de Sitter gravity and spin 3 massless fields in Vasiliev's frame-like formalism. The model is based on vertex operators generating vielbein and connection fields in the Mac Dowell - Mansoury - Stelle - West (MMSW) formulation of gravity. The structure of the vertex operators is based on the hidden symmetry generators in RNS superstring theory, realizing the isometry group of the AdS space. The beta-function equations in the sigma-model lead to equations of motion in the MMSW gravity with negative cosmological constant with the AdS geometry being the vacuum solution. Generalizations for the higher spin fields are analyzed and equations of motion for spin 3 fields in $d=3$ in frame-like formalism are obtained in the low energy limit of string theory. These equations correspond to those of $sl(3,R)$ truncated Chern-Simons action based on higher spin algebra $hs(1,1)$.

21 pages typos corrected, few clarifications and references added

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Cited by in corpus (15)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Cubic interactions of massless higher spins in (A)dS: metric-like approach
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
• Generating functions of (partially-)massless higher-spin cubic interactions
• Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds
• Off-shell massive N=1 supermultiplets in three dimensions
• Spin-3 Topological Massive Gravity
• Multiparticle extension of the higher-spin algebra
• High Spin Topologically Massive Gravity
• On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields
• String Amplitudes and Frame-like Formalism for Higher Spins
• Higher Spin Holography and AdS String Sigma-Model
• Higher Spins at the Quintic Order: Localization Effect and Simplifications
• Higher Spin Contributions to Holographic Fluid Dynamics in $Ad{S}_5/CF{T}_4$