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arXiv · 2610.28183

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

Bruce A. Bassett·Sergio Cacciatori·Ugo Moschella
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Abstract

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.

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Bruce A. Bassett, Sergio Cacciatori, Ugo Moschella. 2026-10-20. Finite Spectral Recurrences for Loop Integrals in de Sitter and Anti-de Sitter Space. https://arxiv.org/abs/2610.28183

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