Finite Spectral Recurrences for Loop Integrals in de Sitter and Anti-de Sitter Space

@misc{bassett2026finite,
  title = {{Finite Spectral Recurrences for Loop Integrals in de Sitter and Anti-de Sitter Space}},
  author = {Bruce A. Bassett and Sergio Cacciatori and Ugo Moschella},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28183},
  eprint = {2610.28183},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28183},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Finite Spectral Recurrences for Loop Integrals in de Sitter and Anti-de Sitter Space
AU  - Bruce A. Bassett
AU  - Sergio Cacciatori
AU  - Ugo Moschella
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28183
UR  - https://arxiv.org/abs/2610.28183
AB  - We introduce a method that does for loop integrals in de Sitter and anti-de Sitter space what integration-by-parts identities do in flat space. A local, coordinate-free propagator algebra common to both geometries yields exact finite-difference equations in spectral labels; with external points they become differential-difference equations, and at the AdS boundary recover known Witten-diagram relations. Acting line by line, they apply in principle to any diagram. We solve them for the two-loop watermelon, isolating its ultraviolet poles, and for one-loop two- and four-point functions.
ER  -