Random Euclidean CFT2 from Triangulated dS3 Gravity
Abstract
We propose a random Euclidean CFT description of three-dimensional de Sitter gravity with fixed central charge and primary spectrum but fluctuating OPE coefficients. A normalized four-point coefficient extracted from the complex Liouville cosmological wavefunction matches the analytically continued tetrahedral Virasoro graph amplitude. Its two-copy form gives a non-Gaussian OPE correlation, with a modular S transform relating the corresponding amplitude to fixed-angle Conformal Turaev--Viro theory. The K4 graph also determines a compact hyperbolic core assembled from two generalized tetrahedra, with a pleated genus-three boundary. We reconstruct this core directly from a marked family of real Lorentzian de Sitter spacetimes expanding from a tetrahedral initial graph. Inverse normal flow collapses six future-boundary collars into geodesic cuffs. Initial spacelike arc lengths fix the exterior dihedral angles, while boost holonomies and marked seams determine the edge lengths and face pairings. Semiclassically, the OPE correlation acquires an oscillatory phase governed by hyperbolic volume, whose angle derivatives measure Lorentzian holonomies. As four necks of the future boundary pinch and the remaining bends vanish, its genus-three surface degenerates into two four-punctured spheres joined at four nodes. Sphere-tree sewing extends this relation between geometry and wavefunction coefficients to higher-point channels.
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BibTeX
@misc{chae2026random,
title = {{Random Euclidean CFT$_2$ from Triangulated dS$_3$ Gravity}},
author = {Ji-seong Chae},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30126},
eprint = {2610.30126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30126},
}
RIS
TY - UNPB
TI - Random Euclidean CFT_2 from Triangulated dS_3 Gravity
AU - Ji-seong Chae
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.30126
UR - https://arxiv.org/abs/2610.30126
AB - We propose a random Euclidean CFT description of three-dimensional de Sitter gravity with fixed central charge and primary spectrum but fluctuating OPE coefficients. A normalized four-point coefficient extracted from the complex Liouville cosmological wavefunction matches the analytically continued tetrahedral Virasoro graph amplitude. Its two-copy form gives a non-Gaussian OPE correlation, with a modular S transform relating the corresponding amplitude to fixed-angle Conformal Turaev--Viro theory. The K_4 graph also determines a compact hyperbolic core assembled from two generalized tetrahedra, with a pleated genus-three boundary. We reconstruct this core directly from a marked family of real Lorentzian de Sitter spacetimes expanding from a tetrahedral initial graph. Inverse normal flow collapses six future-boundary collars into geodesic cuffs. Initial spacelike arc lengths fix the exterior dihedral angles, while boost holonomies and marked seams determine the edge lengths and face pairings. Semiclassically, the OPE correlation acquires an oscillatory phase governed by hyperbolic volume, whose angle derivatives measure Lorentzian holonomies. As four necks of the future boundary pinch and the remaining bends vanish, its genus-three surface degenerates into two four-punctured spheres joined at four nodes. Sphere-tree sewing extends this relation between geometry and wavefunction coefficients to higher-point channels.
ER -