Integral relations for arbitrary AdS vertex-function topologies

Formulate integral relations between $(n-1)$-point and $n$-point AdS vertex functions for every topology of AdS vertex functions, thereby enabling application of the reduction technique to arbitrary $n$-point AdS Feynman diagrams.

Background

The reduction technique recursively decomposes an $n$-point AdS Feynman diagram by expressing it in terms of $(n-1)$-point diagrams and then converting integrals of $(n-1)$-point AdS vertex functions into $n$-point AdS vertex functions. The paper establishes the required relations for the comb channel and derives a five-point relation involving a modified propagator, which suffices for the five-point examples and can be extended recursively to certain diagrams composed entirely of cubic vertices.

For arbitrary $n$-point topologies, however, the necessary integral relations have not been formulated. Developing such relations would extend the reduction technique beyond the comb-channel and recursively tractable cubic cases to general AdS Feynman diagrams.