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On the analytic continuation and asymptotic behaviour of the two-point function in massless ϕ4-theory in Euclidean de Sitter space

  • Martin Beneke
  • Andrea F. Sanfilippo
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Abstract

For the two-point function of the massless, minimally-coupled, real scalar field in Euclidean de Sitter space with λϕ4-interaction, we compute the leading-logarithmic terms in the invariant distance of the two-point function to O(λ2), which counts as the fifth subleading order (N5LO) in the √λ-expansion. We show that the analytic continuation to Lorentzian signature coincides with the expansion of the analogous quantity computed in the stochastic formalism. We determine the large-order behaviour of the stochastic series expansion and prove its Borel summability, which suggests that the Euclidean theory can be used to extract the late-time behaviour of massless correlation functions in Lorentzian de Sitter space.

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Cite

BibTeXRIS
BibTeX
@misc{beneke2026analytic,
  title = {{On the analytic continuation and asymptotic behaviour of the two-point function in massless $ϕ^4$-theory in Euclidean de Sitter space}},
  author = {Martin Beneke and Andrea F. Sanfilippo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17215},
  eprint = {2610.17215},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17215},
}
RIS
TY  - UNPB
TI  - On the analytic continuation and asymptotic behaviour of the two-point function in massless ϕ^4-theory in Euclidean de Sitter space
AU  - Martin Beneke
AU  - Andrea F. Sanfilippo
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17215
UR  - https://arxiv.org/abs/2610.17215
AB  - For the two-point function of the massless, minimally-coupled, real scalar field in Euclidean de Sitter space with λϕ^4-interaction, we compute the leading-logarithmic terms in the invariant distance of the two-point function to O(λ^2), which counts as the fifth subleading order (N^5LO) in the √λ-expansion. We show that the analytic continuation to Lorentzian signature coincides with the expansion of the analogous quantity computed in the stochastic formalism. We determine the large-order behaviour of the stochastic series expansion and prove its Borel summability, which suggests that the Euclidean theory can be used to extract the late-time behaviour of massless correlation functions in Lorentzian de Sitter space.
ER  -