Building up quantum spacetimes with BCFT Legos

• URL: http://arxiv.org/abs/2404.00877v1
• Date: Mon, 1 Apr 2024 03:14:36 GMT
• Title: Building up quantum spacetimes with BCFT Legos
• Authors: Ling-Yan Hung, Yikun Jiang,
• Abstract summary: We show that it is possible to read off the quantum gravity dual of a CFT directly from its operator algebra. We present a step-by-step recipe results and techniques from conformal bootstrap, topological symmetries, tensor networks, and novel symmetry-preserving real-space renormalization algorithm.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Is it possible to read off the quantum gravity dual of a CFT directly from its operator algebra? In this essay, we present a step-by-step recipe synthesizing results and techniques from conformal bootstrap, topological symmetries, tensor networks, a novel symmetry-preserving real-space renormalization algorithm devised originally in lattice models, and the asymptotics of quantum $6j$ symbols, thereby providing an answer in the affirmative. Quantum 2D Liouville theory serves as a simple and explicit example, illustrating how the quantum gravitational path integral can be built up from local pieces of BCFT correlation functions, which we call the ``BCFT Legos''. The constructive map between gravity and CFT naturally and explicitly bridges local geometrical data, algebraic structures, and quantum entanglement, as envisaged by the $\it{It \, from \, Qubit}$ motto.

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