On two pieces of folklore in the AdS/CFT duality

Understand

In the AdS/CFT duality, it is often said that a local symmetry in a bulk theory corresponds to a global symmetry in the corresponding boundary theory, but the global symmetry can become local when one couples with an external source.

• As a result, the GKP-Witten relation gives a response function instead of a Green function.
• We explore this point in details using the example of holographic superconductors.
• We point out that these points play a crucial role to interpret the holographic London equation properly.