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arXiv · 2610.30247

3D de Sitter from complex Virasoro TQFT: Observers and knots

Jeevan Chandra·Diego Liska·Boris Post
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Abstract

The Euclidean saddles of 3D Einstein gravity with positive cosmological constant are spherical three-manifolds. When one adds a heavy observer, the backreacted saddles are spherical cone manifolds, with a conical singularity along the observer worldline. We propose exact gravitational partition functions at fixed topology on a class of spherical cone manifolds that undergo hyperbolic-to-spherical transitions as the cone angles increase. Our construction relies on a careful analytic continuation of the product of two Virasoro TQFT partition functions. We test the proposal by showing that the exact partition functions exponentiate in the semiclassical limit to the spherical volume, in agreement with the gravitational on-shell action. This leads to a spherical volume conjecture for the product of continued Virasoro TQFT amplitudes. As further evidence, we relate the theta and tetrahedron graph amplitudes to the two-point function and out-of-time-ordered four-point function of operators on a massive observer's worldline. In appropriate limits, we recover the static patch scalar two-point function with finite observer backreaction and the semiclassical effects of observer recoil. In addition, we analyze examples with knotted worldlines and reproduce their spherical volumes. We also apply our prescription to Seifert manifolds, which are off-shell in AdS$_3$ gravity but admit dS$_3$ saddles, and find agreement with their spherical volumes semiclassically. Finally, using Dehn surgery on torus knots and links, we obtain partition functions on smooth spherical three-manifolds.

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Jeevan Chandra, Diego Liska, Boris Post. 2026-10-21. 3D de Sitter from complex Virasoro TQFT: Observers and knots. https://arxiv.org/abs/2610.30247

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