A String Model for AdS Gravity and Higher Spins

TL;DR

This paper develops a string sigma-model that describes AdS gravity and massless spin 3 fields, deriving their equations of motion from the low energy limit of string theory and connecting to higher spin algebra structures.

Contribution

It constructs a string-based model capturing AdS gravity and higher spin fields within the MMSW formalism, linking string theory vertex operators to higher spin equations of motion.

Findings

Derivation of AdS gravity equations from the sigma-model beta-functions.

Extension of the model to include spin 3 fields in three dimensions.

Connection of the equations of motion to higher spin algebra and Chern-Simons theory.

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 $hs(1,1)$.