Bootstrapping Pure Quantum Gravity in AdS3

Abstract

The three-dimensional pure quantum gravity with negative cosmological constant is supposed to be dual to the extremal conformal field theory of central charge $c=24k$ in two dimensions. We employ the conformal bootstrap method to analyze the extremal CFTs, and find numerical evidence for the non-existence of the extremal CFTs for sufficiently large central charge ($k\ge 20$). We also explore near-extremal CFTs, a small modification of extremal ones, and find similar evidence for their non-existence for large central charge. This indicates, under the assumption of holomorphic factorization, the pure gravity in the weakly curved AdS${}_3$ do not exist as a consistent quantum theory.

16 pages, 3 figures

References in corpus (11)

• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Three-Dimensional Gravity Revisited
• Bootstrapping the O(N) Vector Models
• Meromorphic c=24 Conformal Field Theories
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Constraints on extremal self-dual CFTs
• A Semidefinite Program Solver for the Conformal Bootstrap
• N=4 Superconformal Bootstrap of the K3 CFT
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity
• Modular Bootstrap Revisited

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• Modular Constraints on Conformal Field Theories with Currents
• Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Generic AdS3 Black Holes
• Monstrous entanglement
• Analytic Studies of Fermions in the Conformal Bootstrap