TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.6.163
TI  - Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
PY  - 2025/12/23
UR  - https://scipost.org/SciPostPhys.19.6.163
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 6
SP  - 163
A1  - Chen, Lin
AU  - Hung, Ling-Yan
AU  - Jiang, Yikun
AU  - Lao, Bing-Xin
AB  - 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},
}