Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS

Abstract

In this paper we consider Witten diagrams at one loop in AdS space for scalar ${\varphi }^3+{\varphi }^4$ theory. After using Schwinger parametrization to trivialize the space-time loop integration, we extract the Mellin-Barnes representation for the one-loop corrections to the four-particle scattering up to an integration over the Schwinger parameters corresponding to the propagators of the internal particles running into the loop. We then discuss an approach to deal with those integrals.

arXiv comment27 pages, 6 figures. References added, typos corrected

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• Anatomy of Geodesic Witten Diagrams
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• Holographic dual of the five-point conformal block
• Loops in AdS: From the Spectral Representation to Position Space
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• OPE inversion in Mellin space