Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra, by Lin Chen, Ling-Yan Hung, Yikun Jiang, Bing-Xin Lao

SciPost Physics Home Authoring Refereeing Submit a manuscript About Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra Lin Chen, Ling-Yan Hung, Yikun Jiang, Bing-Xin Lao SciPost Phys. 19, 163 (2025) · published 23 December 2025 doi: 10.21468/SciPostPhys.19.6.163 pdf BiBTeX RIS Submissions/Reports Abstract We demonstrate that, by utilizing the boundary conformal field theory (BCFT) operator algebra of the Liouville CFT, one can express its path-integral on any Riemann surface as a three dimensional path-integral with appropriate boundary conditions, generalising the recipe for rational CFTs. This serves as a constructive method for deriving the quantum holographic dual of the CFT, which reduces to Einstein gravity in the large central charge limit. As a byproduct, the framework provides an explicit discrete state-sum of a 3D non-chiral topological theory constructed from quantum $6j$ symbols of $\mathcal{U}_q(sl(2,\mathbb{R}))$ with non-trivial boundary conditions, representing a long-sought non-perturbative discrete formulation of 3D pure gravity with negative cosmological constant, at least within a class of three manifolds. This constitutes the first example of an exact holographic tensor network that reproduces a known irrational CFT with a precise quantum gravitational interpretation. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.6.163TI - Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebraPY - 2025/12/23UR - https://scipost.org/SciPostPhys.19.6.163JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 6SP - 163A1 - Chen, LinAU - Hung, Ling-YanAU - Jiang, YikunAU - Lao, Bing-XinAB - We demonstrate that, by utilizing the boundary conformal field theory (BCFT) operator algebra of the Liouville CFT, one can express its path-integral on any Riemann surface as a three dimensional path-integral with appropriate boundary conditions, generalising the recipe for rational CFTs. This serves as a constructive method for deriving the quantum holographic dual of the CFT, which reduces to Einstein gravity in the large central charge limit. As a byproduct, the framework provides an explicit discrete state-sum of a 3D non-chiral topological theory constructed from quantum $6j$ symbols of $\mathcal{U}_q(sl(2,\mathbb{R}))$ with non-trivial boundary conditions, representing a long-sought non-perturbative discrete formulation of 3D pure gravity with negative cosmological constant, at least within a class of three manifolds. This constitutes the first example of an exact holographic tensor network that reproduces a known irrational CFT with a precise quantum gravitational interpretation.ER - × @Article{10.21468/SciPostPhys.19.6.163, title={{Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra}}, author={Lin Chen and Ling-Yan Hung and Yikun Jiang and Bing-Xin Lao}, journal={SciPost Phys.}, volume={19}, pages={163}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.6.163}, url={https://scipost.org/10.21468/SciPostPhys.19.6.163},} Disclosure of Generative AI use The author(s) disclose that the following generative AI tools have been used in the preparation of this publication: Used to polish the language of the paper. Ontology / Topics See full Ontology or Topics database. AdS$_3$ gravity AdS/CFT correspondence Conformal field theory (CFT) Renormalization group (RG) Tensor networks Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Lin Chen, 3 4 Ling-Yan Hung, 5 Yikun Jiang, 6 7 8 9 10 Bing-Xin Lao 1 华南理工大学 / South China University of Technology [SCUT] 2 宁波大学 / Ningbo University [NBU] 3 北京应用数学研究院 / Beijing Institute of Mathematical Sciences and Applications [BIMSA] 4 Yau Mathematical Sciences Center [YMSC] 5 Northeastern University [NEU] 6 Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS] 7 Laboratoire de Physique Théorique et Hautes Energies / Laboratory of Theoretical and High Energy Physics [LPTHE] 8 Université de recherche Paris Sciences et Lettres / PSL Research University [PSL] 9 Sorbonne Université / Sorbonne University 10 École Normale Supérieure [ENS] Funders for the research work leading to this publication Key Technologies Research and Development Program of Guangzhou Municipality National Natural Science Foundation of China [NSFC]