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arXiv · 2605.06542

de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs

Livia Ferro·Tomasz Lukowski·Lecheng Ren·Marcus Spradlin·Anastasia Volovich·He-Chen Weng·Yao-Qi Zhang
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Abstract

We present an explicit formula for the $n$-site chain graph contribution to the cosmological wavefunction for conformally coupled $\phi^3$ theory in de Sitter space. Our result relies on the recent finding that the symbol of this function satisfies total compatibility with respect to the $A_{2n-2}$ cluster algebra, and that Rudenko's quadrangular polylogarithms provide, by construction, a complete basis for such functions. We prove our formula by directly relating a recursive set of differential equations satisfied by these wavefunction coefficients to a recursive coproduct formula for quadrangular polylogarithms.

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Livia Ferro, Tomasz Lukowski, Lecheng Ren, Marcus Spradlin, Anastasia Volovich, He-Chen Weng, Yao-Qi Zhang. 2026-05-07. de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs. https://arxiv.org/abs/2605.06542

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