Notes on flat-space limit of AdS/CFT

Understand

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion.

• We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS.
• In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion.
• Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks.