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arXiv · 2404.00877

Building up quantum spacetimes with BCFT Legos

Ling-Yan Hung·Yikun Jiang
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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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Ling-Yan Hung, Yikun Jiang. 2024-04-01. Building up quantum spacetimes with BCFT Legos. https://arxiv.org/abs/2404.00877

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