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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Generalised cluster adjacency for cosmology

  • Mattia Capuano1
  • Livia Ferro1
  • Tomasz Łukowski1
  • Alessandro Palazio1
  • Yao-Qi Zhang1
  1. 1University of Hertfordshire
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Abstract

In this paper we study the cluster algebraic properties of wavefunction coefficients for conformally coupled scalar theories in de Sitter cosmology. We show that the symbol of the wavefunction coefficient of the n-site chain graph Pn obeys a generalisation of cluster adjacency, where all letters in a given word belong to the same cluster of an A2n−3 algebra, with certain additional constraints on the order of the letters. We call this property the ordered single cluster condition, and provide its physical interpretation. This condition is stronger than the usual cluster adjacency obeyed by neighbouring letters, and thereby constrains the symbol bootstrap far more tightly. We also show that for an arbitrary graph the alphabet carries a cluster-like structure, described by tubes and tubings on the graph, which allows for a similar bootstrap approach.

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Cite

BibTeXRIS
BibTeX
@article{capuano2026generalised,
  title = {{Generalised cluster adjacency for cosmology}},
  author = {Mattia Capuano and Livia Ferro and Tomasz Łukowski and Alessandro Palazio and Yao-Qi Zhang},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)010},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)010},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Generalised cluster adjacency for cosmology
AU  - Mattia Capuano
AU  - Livia Ferro
AU  - Tomasz Łukowski
AU  - Alessandro Palazio
AU  - Yao-Qi Zhang
PY  - 2026
DA  - 2026/11/02
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)010
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)010
AB  - In this paper we study the cluster algebraic properties of wavefunction coefficients for conformally coupled scalar theories in de Sitter cosmology. We show that the symbol of the wavefunction coefficient of the n-site chain graph Pn obeys a generalisation of cluster adjacency, where all letters in a given word belong to the same cluster of an A2n−3 algebra, with certain additional constraints on the order of the letters. We call this property the ordered single cluster condition, and provide its physical interpretation. This condition is stronger than the usual cluster adjacency obeyed by neighbouring letters, and thereby constrains the symbol bootstrap far more tightly. We also show that for an arbitrary graph the alphabet carries a cluster-like structure, described by tubes and tubings on the graph, which allows for a similar bootstrap approach.
SN  - 1029-8479
ER  -