BCFW for Witten Diagrams
Suvrat Raju
TL;DR
The paper extends the BCFW recursion relations to AdS spaces to efficiently compute sums of tree-level Witten diagrams, enabling new recursion relations for boundary CFT correlators in AdS/CFT with p>4. It introduces transition amplitudes between bulk normalizable states and boundary data, and demonstrates a decomposition of higher-point amplitudes into products of lower-point amplitudes with an internal propagator, including a boundary term for scalar cases. The authors extend the framework to Yang-Mills and gravity in AdS, deriving polarization constraints that ensure good large-w behavior and leading to boundary-free recursion that ultimately reduces to three-point amplitudes; supersymmetry further expands computable correlators via on-shell superspace. They outline results for d=4,5,6 and discuss future work to access higher-order correlators and potential extensions beyond tree level.
Abstract
We show that a generalization of the BCFW recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an AdS_p dual, for p > 4, in the limit where the bulk theory is approximated by tree-level Yang-Mills or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.