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# Towards higher-spin AdS$_2$/CFT$_1$ holography

Abstract : We aim at formulating a higher-spin gravity theory around AdS$_{2}$ relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by [λ] and parameterized by a real parameter λ. The singleton is defined to be a Verma module of the AdS$_{2}$ isometry subalgebra so (2, 1) ⊂ [λ] with conformal weight $\Delta =\frac{1\pm \lambda }{2}.$ On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS$_{2}$ with ascending masses expressed in terms of λ. On the other hand, the higher-spin fields arising through the gauging of [λ] algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS$_{2}$ higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT$_{1}$ duals of the kinematical structures identified in the bulk.
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https://hal.archives-ouvertes.fr/hal-02416899
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Submitted on : Tuesday, December 17, 2019 - 9:12:43 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:11 PM

### Citation

Konstantin Alkalaev, Xavier Bekaert. Towards higher-spin AdS$_2$/CFT$_1$ holography. Journal of High Energy Physics, Springer, 2020, 04, pp.206. ⟨10.1007/JHEP04(2020)206⟩. ⟨hal-02416899⟩

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