Multi-centered higher spin solutions from $W_N$ conformal blocks

Abstract

Motivated by the question of bulk localization in holography, we study the problem of constructing multi-centered solutions in higher spin gravity which describe point particles in the interior of AdS${}_3$. In the Chern-Simons formulation these take into account the backreaction after adding Wilson line sources. We focus on chiral solutions where only the left-moving sector is excited. In that case it is possible to choose a gauge where the dynamical variables are a set of Toda fields living in the bulk. The problem then reduces to solving the ${\mathcal{A}}_{N-1}$ Toda equations with delta function sources, which in turn requires solving an associated monodromy problem. We show that this monodromy problem is equivalent to the monodromy problem for a particular ${\mathcal{W}}_N$ vacuum conformal block at large central charge. Therefore, knowledge of the ${\mathcal{W}}_N$ vacuum block determines the multi-centered solution. Our calculations go beyond the heavy-light approximation by including the backreaction of all higher spin particles.

arXiv comment46 pages, 1 figure

References in corpus (22)

• Black Holes: Complementarity or Firewalls?
• Holographic representation of local bulk operators
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• An Infalling Observer in AdS/CFT
• Analytic Continuation of Liouville Theory
• Three-dimensional quantum geometry and black holes
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Correlation functions in conformal Toda field theory I
• Conformal Bootstrap, Universality and Gravitational Scattering
• Holographic entanglement entropy and gravitational anomalies
• Higher Spin Entanglement and W_N Conformal Blocks
• Holographic conformal blocks from interacting Wilson lines
• Null vectors, 3-point and 4-point functions in conformal field theory
• The large central charge limit of conformal blocks
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Quantizing higher-spin gravity in free-field variables
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$

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• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• More on Wilson toroidal networks and torus blocks
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Information recovery from pure state geometries in 3D
• Holography for bulk states in 3D quantum gravity
• Example of the $4$-pt non-vacuum ${\mathcal{W}}_3$ classical block