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

Abstract

We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar ${\varphi }^4$-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.

Latex. 65 pages. v2: minor corrections, version to appear in JHEP

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• Bulk renormalization and the AdS/CFT correspondence
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• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space