Boundary Holographic Witten Diagrams

TL;DR

This paper develops a holographic dual description of boundary conformal field theory two-point functions using geodesic Witten diagrams, providing a geometric understanding of boundary and ambient channel decompositions.

Contribution

It derives a holographic dual for the boundary channel decomposition in terms of bulk-to-bulk propagators on lower-dimensional AdS slices, extending previous work.

Findings

Derived holographic dual of boundary channel decomposition.

Calculated leading corrections to two-point functions in boundary and ambient channels.

Reproduced conformal block decompositions using geodesic Witten diagrams.

Abstract

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.