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arXiv · 2512.15852

On Positive Celestial Geometry: ABHY in the Sky

Jin Dong·Stephan Stieberger
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Abstract

Celestial amplitudes are multiple Mellin transforms w.r.t. conformal dimensions. For arbitrary multiplicity $n$ of massless states in sufficiently high space--time dimension $D$ we perform all Mellin integrations and find an associahedron description in celestial space. The latter expresses celestial tree--level $\phi^3$ amplitudes as the canonical forms associated with this positive geometry. This yields a geometric interpretation of celestial amplitudes in terms of the underlying boundary geometry. Our universal treatment of Mellin integrals in $D$ dimensions also provides a unified description of celestial amplitudes arising from different bulk theories.

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Jin Dong, Stephan Stieberger. 2025-12-17. On Positive Celestial Geometry: ABHY in the Sky. https://arxiv.org/abs/2512.15852

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