AdS/CFT for 3D Higher-Spin Gravity Coupled to Matter Fields

Abstract

New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu \nu }$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. By using a local symmetry, two of the components of $B_{\mu \nu }$ are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, $B_{\varphi \rho }$, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields $A_{\mu }$, ${\bar{A}}_{\mu }$. In this model, solutions to the classical equations of motion for $A_{\mu }$ and ${\bar{A}}_{\mu }$ are non-flat due to the interactions with matter fields. The solutions for the gauge fields can, however, be split into two parts, flat gauge fields ${\mathcal{A}}_{\mu }$, ${\bar{\mathcal{A}}}_{\mu }$, and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds ${\mathcal{A}}_{\mu }$ and ${\bar{\mathcal{A}}}_{\mu }$, which are exactly the same as those in linearized 3d Vasiliev gravity. The two- and three-point correlation functions of operators in the boundary CFT are computed by using an on-shell action, $\text{tr}(B_{\varphi \rho }C)$. This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the near-boundary limit $\rho \to \infty$. Analysis is presented for SL(3,R) $\times$ SL(3,R) as well as $HS[\frac{1}{2}]\times HS[\frac{1}{2}]$ higher-spin gravity. In the latter model, scalar operators with scaling dimensions ${\Delta }_{+}=\frac{3}{2}$ and ${\Delta }_{-}=\frac{1}{2}$ appear in a single quantization.

35 pages, no figures;v2 a footnote and a reference added

References in corpus (6)

• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Higher Spins in AdS and Twistorial Holography
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence

Cited by in corpus (9)

• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Spectral Flow in 3D Flat Spacetimes
• 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory
• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• Higher-spin gauge theories in three spacetime dimensions
• Quantization of a Scalar Field in Two Poincaré Patches of Anti-de Sitter Space and AdS/CFT
• Anomaly of Tensionless String in Light-cone Gauge
• Ising Model on Twisted Lattice and Holographic RG flow