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Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals

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arxiv 2201.09626 v2 pith:ZTSV76NP submitted 2022-01-24 hep-th

Till Heckelbacher , Ivo Sachs , Evgeny Skvortsov , Pierre Vanhove This is my paper · ORCID
classification hep-th
keywords diagramswittenflatspaceevaluationfeynmanintegralsmulti-loop
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar $\phi^4$-theory in Euclidean AdS$_4$, by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classical conformal invariance and superhorizon dynamics in de Sitter

    hep-th 2026-07 conditional novelty 6.5 of 10

    Standard SdSET power counting fails for classically conformal φ⁴; leading superhorizon modes must be read from the two-loop anomalous dimension of the two-point function.

  2. Bulk-to-bulk photon propagator in AdS

    hep-th 2025-10 unverdicted novelty 6.0 of 10

    The bulk-to-bulk photon propagator in Euclidean AdS is derived in axial, Coulomb and covariant gauges, with the simplest position-space form in the Fried–Yennie gauge ξ=d/(d−2).

  3. Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module

    hep-th 2025-06 conditional novelty 6.0 of 10

    A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

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