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 Bμν and C, which was introduced in Fujisawa and Nakayama (2014 Class. Quantum Grav. 31 015003), is formulated. By using a local symmetry, two of the components of Bμν are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, Bϕρ, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields Aμ, . In this model, solutions to the classical equations of motion for Aμ and 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 , , 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 and , which are exactly the same as those in linearized 3d Vasiliev gravity. The two- and three-point correlation functions of the single-trace operators and the higher-spin currents in the boundary CFT are computed by using an on-shell action tr (Bϕρ 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 ρ → ∞. Analysis is presented for SL(3,R) × SL(3,R) as well as higher-spin gravity. In the latter model, scalar operators with scaling dimensions Δ+ = 3/2 and Δ− = 1/2 appear in a single quantization.