Boundary Holographic Witten Diagrams

Understand

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect.

• Boundary CFTs allow two different decompositions of two-point functions into conformal blocks: boundary channel and ambient channel.
• Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices.
• In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams which exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.