AdS/CFT for 3D higher-spin gravity coupled to matter fields

DOI10.1088/0264-9381/31/6/065006zbMATH Open1292.83041arXiv1311.4714OpenAlexW2073160098MaRDI QIDQ5413618

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Publication date: 30 April 2014

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Abstract: New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{muu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. By using a local symmetry, two of the components of $B_{muu}$ are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, $B_{phiho}$, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields $A_{mu}$, $$. In this model, solutions to the classical equations of motion for $A_{mu}$ and $$ 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 ${calA}_{mu}$, $$, and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds ${calA}_{mu}$ and $$, 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, $exttr,(B_{phiho},C)$. 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 $hoightarrowinfty$. Analysis is presented for SL(3,R) $imes$ SL(3,R) as well as $HS[frac12]imesHS[frac12]$ higher-spin gravity. In the latter model, scalar operators with scaling dimensions $Delt{a}_{+}=frac32$ and $Delt{a}_{-}=frac12$ appear in a single quantization.

Full work available at URL: https://arxiv.org/abs/1311.4714

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