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

TL;DR

This paper presents a systematic method to evaluate AdS$_4$ Witten diagrams by translating them into flat space Feynman integrals, deriving anomalous dimensions, and connecting boundary expansion discontinuities with flat space unitarity methods.

Contribution

It introduces a novel approach to compute multi-loop Witten diagrams in AdS$_4$ by expressing them as flat space Feynman integrals, enabling explicit anomalous dimension calculations.

Findings

Derived closed-form expressions for anomalous dimensions of double-trace operators.

Established a connection between boundary expansion discontinuities and flat space unitarity.

Provided a systematic framework for evaluating multi-loop AdS Witten diagrams.

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.