Towards higher-spin AdS2/CFT1 holography
Konstantin Alkalaev, Xavier Bekaert
Abstract
A bstract 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 $$ \Delta =\frac{1\pm \lambda }{2}. $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>±</mml:mo> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>.</mml:mo> </mml:math> 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.