Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

By Andrea Campoleoni, S. Fredenhagen, Stefan Pfenninger, S. Theisen. 2010

710 citations recorded by the source corpus.

We discuss the emergence of $ \mathcal{W} \mbox{-algebras}$ as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) × SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical $ {\mathcal{W}_3}\mbox{-algebra} $ with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6ad0d71e8c488cd952c9ada303e6b3e55dc27dfc

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Citations in the corpus

Partition functions of higher spin black holes and their CFT duals (2011, methodology): “The spacetime interpretation and asymptotic symmetries of the SL(3,R) × SL(3,R) Chern-Simons theory were treated in detail in [29], following which [17,18] discovered smooth, asymptotically AdS3, black hole solutions with nonzero spin-3 charge and consistent thermodynamics.”
Generalized black holes in three-dimensional spacetime (2014, background): “As shown in [14, 15], the boundary conditions (5.”
Higher spin black holes (2011, methodology): “4 Our L and L are defined with opposite sign relative to those in [15].”
Effective action in a higher-spin background (2010, background): “Notice that the case of AdS3/CFT2 is special in this respect [23].”
Triality in minimal model holography (2012, background): “The particular cases studied in [3, 4] actually belong to a one-parameter family of higher spin theories whose symmetry algebras could be identified with W∞[μ] [5] (see also [6]).”
Higher spins & strings (2014, background): “We believe the AdS3/CFT2 case is particularly suited for this endeavour, because, unlike in higher dimensions, the higher spin symmetry group is enlarged here to aW∞ algebra [21, 22, 23] (generalising the enhancement to Virasoro discovered by Brown and Henneaux [24]).”
Semiclassical Virasoro blocks from AdS3 gravity (2015, methodology): “Rather than working in terms of symmetric traceless tensors, it will be extremely convenient to use an equivalent Chern-Simons formulation [28–30].”
Black holes and singularity resolution in higher spin gravity (2011, background): “A full discussion of this prescription can be found in [34, 35, 36], and its implementation in higher spin theories in [37, 23, 38, 33].”
Black holes in three dimensional higher spin gravity: a review (2012, methodology): “The asymptotic symmetries of the higher spin gravity can most easily be obtained by Hamiltonian reduction [44,45,46,41,47,48].”
Higher spin black holes from CFT (2012, background): “In AdS3/CFT2, the duality relates higher spin gravity to CFTs with W-symmetry [7, 8].”
Elements of Vasiliev theory (2014, background): “This field has recently received great deal of attention especially in d = 3, [64–69], and develops rapidly.”
Bounding the space of holographic CFTs with chaos (2016, background): “This includes the oft-studied G = SL(N,R) theories [37], where WSL(N,R) = WN .”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “In this way, it was possible to show that asymptotically they enjoy a W∞(λ) infinite-dimensional symmetry [237, 238], which also characterises minimal models in CFT2 [239], see ref.”
Symmetries of holographic minimal models (2011, methodology): “Following the appearance of W-symmetry in the asymptotic algebra of AdS3 higher spin theories [11, 12, 13], it was proposed that a particular AdS3 higher spin theory together with a pair of massive complex scalar fields is dual to the WN minimal models at large N [14].”
Cubic interactions of massless higher spins in (A)dS: Metric-like approach (2011, background): “24 In the AdS3 case, there has been considerable recent development after the works [94, 95].”