HKLL for the non-normalizable mode

A bstract We discuss various aspects of HKLL bulk reconstruction for the free scalar field in AdS d +1 . First, we consider spacelike kernel non-normalizable mode global coordinates. construct it as a sum. In even dimensions, this can be reproduced using chordal Green’s function approach that propose. This puts results on an equal footing with literature normalizable mode. Poincaré AdS, present explicit sum general and odd dimensions both kernels. For generic scaling dimension ∆, these re-written form matches via antipodal mapping, plus remainder. are not aware argument dropping remainder terms, but note slight complexification boundary spatial coordinate (which call iϵ prescription) allows us to do so cases where ∆ is (half-) integer. Since turns source CFT, our primary motivation considering step towards understanding linear wave equations spacetimes from holographic perspective. But when Breitenlohner-Freedman window, construction has some interesting features within AdS/CFT.