Two pieces of folklore in the AdS/CFT duality

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 Gubser-Klebanov-Polyakov-Witten relation gives a response function instead of a Green function. We explore this point in detail using the example of holographic superconductors. We point out that these points play a crucial role in interpreting the holographic London equation properly.