More on Boundary Holographic Witten Diagrams

TL;DR

This paper extends the analysis of geodesic Witten diagrams in boundary or defect conformal field theories to two-point functions involving different operators, providing new decompositions in both ambient and boundary channels.

Contribution

It generalizes previous work by deriving two distinct conformal block decompositions for two-point functions of different operators in boundary or defect CFTs.

Findings

Derived new conformal block decompositions for mixed operators.

Extended geodesic Witten diagram analysis to more general operator pairs.

Provided a framework for analyzing non-trivial two-point functions in boundary CFTs.

Abstract

In this paper we discuss geodesic Witten diagrams in general holographic conformal field theories with boundary or defect. In boundary or defect conformal field theory, two-point functions are non-trivial and can be decomposed into conformal blocks in two distinct ways; ambient channel decomposition and boundary channel decomposition. In our previous work we only consider two-point functions of same operators. We generalize our previous work to a situation where operators in two-point functions are different. We obtain two distinct decomposition for two-point functions of different operators.