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PreprintCC BY 4.0arXiv

de Sitter Wavefunction from Quadrangular Polylogarithms: Polygon Graphs

  • Livia Ferro
  • Tomasz Lukowski
  • Shruti Paranjape
  • 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-gon graph contribution to the integrand of the cosmological wavefunction for conformally coupled ϕ3 theory in de Sitter space. Our result relies on the fact that its symbol satisfies total compatibility with respect to the B2n−1 cluster algebra. We introduce B-type quadrangular polylogarithms, constructed from centrally symmetric quadrangulations of a 4n-gon, and show that the n-gon wavefunction coefficient is expressed by a natural weight-n function of this class. We prove our formula by directly relating the recursive differential equation satisfied by these wavefunction coefficients to a recursive coproduct formula for B-type quadrangular polylogarithms, with the remaining additive constant fixed by the soft limit.

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Cite

BibTeXRIS
BibTeX
@misc{ferro2026sitter,
  title = {{de Sitter Wavefunction from Quadrangular Polylogarithms: Polygon Graphs}},
  author = {Livia Ferro and Tomasz Lukowski and Shruti Paranjape and Lecheng Ren and Marcus Spradlin and Anastasia Volovich and He-Chen Weng and Yao-Qi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06772},
  eprint = {2610.06772},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06772},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - de Sitter Wavefunction from Quadrangular Polylogarithms: Polygon Graphs
AU  - Livia Ferro
AU  - Tomasz Lukowski
AU  - Shruti Paranjape
AU  - Lecheng Ren
AU  - Marcus Spradlin
AU  - Anastasia Volovich
AU  - He-Chen Weng
AU  - Yao-Qi Zhang
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06772
UR  - https://arxiv.org/abs/2610.06772
AB  - We present an explicit formula for the n-gon graph contribution to the integrand of the cosmological wavefunction for conformally coupled ϕ^3 theory in de Sitter space. Our result relies on the fact that its symbol satisfies total compatibility with respect to the B_2n−1 cluster algebra. We introduce B-type quadrangular polylogarithms, constructed from centrally symmetric quadrangulations of a 4n-gon, and show that the n-gon wavefunction coefficient is expressed by a natural weight-n function of this class. We prove our formula by directly relating the recursive differential equation satisfied by these wavefunction coefficients to a recursive coproduct formula for B-type quadrangular polylogarithms, with the remaining additive constant fixed by the soft limit.
ER  -