Wilson network decomposition of AdS Feynman diagrams in two dimensions

TL;DR

This paper demonstrates that AdS$_2$ Feynman diagrams can be decomposed into Wilson line network operators, revealing a structure similar to conformal block decomposition, with detailed analysis of 3-point scalar diagrams.

Contribution

It introduces a Wilson network decomposition for AdS$_2$ Feynman diagrams, connecting them to conformal block structures and deriving new propagator identities.

Findings

Decomposition of AdS$_2$ Feynman diagrams into Wilson line networks.

Identification of single-trace and double-trace contributions.

Derivation of propagator identities linking different bulk-to-bulk propagators.

Abstract

We show that Feynman diagrams in AdS$_2$ space can be decomposed into infinite series of matrix elements of Wilson line network operators. The case of the 3-point scalar Feynman diagram with endpoints in the bulk is studied in detail. The resulting decomposition is similar to the conformal block decomposition of Witten diagrams, i.e. it comprises a single-trace term and infinite sums of double-trace terms. We derive a number of AdS propagator identities which relate the standard bulk-to-bulk propagators with the modified bulk-to-bulk propagators of two different types responsible for extracting single-trace and double-trace terms.