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.
Highlights
In d-dimensional conformal field theory (CFT), a conformal symmetry is SOðd; 2Þ and two-point functions and three-point functions are completely determined up to prefactors
Intermediate points among a bulk-to-bulk propagator and two bulk-to-boundary propagators in Witten diagrams are integrated in a whole region of anti-de Sitter (AdS) spacetime, but similar points in geodesic Witten diagrams are integrated along geodesics connecting two boundary points
In this subsection we mainly focus on two-point functions and boundary operator product expansion from the viewpoint of a CFT side
Summary
In d-dimensional conformal field theory (CFT), a conformal symmetry is SOðd; 2Þ and two-point functions and three-point functions are completely determined up to prefactors. Two-point functions are decomposed by two-point functions of boundary operators. This decomposition is called the boundary channel decomposition. Simple holographic models of bCFTs or dCFTs are described by a (d þ 1)-dimensional metric ds2 1⁄4 dr þ e2AðrÞds2AdSd with ds2AdSd. where r is a radial coordinate and r → Æ∞ corresponds to an AdS boundary (see Fig. 1). Our previous paper [4] discussed geodesic Witten diagrams in situations where boundaries or defects are introduced by nontrivial profiles of backgrounds fields on the pure AdS background. We review two distinct decompositions of twopoint functions in CFT side and a holographic dual of boundary OPE.
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