2025/12/21 by Ugo Moschella, Moschella, Ugo
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · doi:10.48550/arxiv.2512.18672
openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
We construct a manifestly covariant and coordinate-free plane-wave representation of scalar two-point functions in d-dimensional anti-de Sitter spacetime. The construction is based on a new class of holomorphic plane waves defined globally on the universal covering of the AdS via chiral cones in the complex null cone. Imposing AdS invariance, locality, positive definiteness and a spectral condition, we obtain integral representations as superpositions over relative homology cycles reproducing the standard maximally analytic solutions in terms of Legendre functions of the second kind. In Poincaré coordinates, the two-point functions diagonalize into a Kallen-Lehmann superposition of (d-1)-dimensional Minkowski correlators where the weight is a product of Bessel functions. This diagonalization clarifies the relation between Euclidean and Lorentzian AdS quantum field theory and allows Wick rotation of Euclidean Feynman diagrams to Lorentzian integrals supported on a single Poincare patch while preserving full AdS covariance.