Reduction technique for expanding the Feynman diagrams in AdS$_2$

Abstract

We formulate the reduction technique for expanding the $n$-point AdS Feynman diagrams in two dimensions into the Wilson line networks. The technique applies to any $n$-point tree diagram, expressing it as several series of the matrix elements of Wilson line network operators, and employs the Wilson network expansions of the $(n-1)$-point AdS Feynman diagrams, which can in turn be obtained using the same technique. Consequently, the complexity of this technique does not increase with $n$, provided that the expansions of the $(n-1)$-point diagrams are known. To demonstrate the reduction technique, we apply it to all topologically distinct five-point AdS Feynman tree diagrams. The resulting expansions near the conformal boundary reproduce the known decompositions of the corresponding five-point Witten diagrams into conformal blocks.