The most intuitive example of a gauge symmetry is such where you take a theory that has some global symmetry, and ask what needs to be done for this symmetry to be local. This procedure involves the introduction of new fields. For example, when a global phase symmetry becomes local, you must include the four-potential and the E.M. field (Or EM-like field?).
- Is a vector field the only result of this procedure? Can, for example, the metric field and invariance to local change of coordinates, be obtained from a promotion of a global symmetry (global change of coordinates I assume?) to a local one?
- What are common examples of gauge symmetries that do not emerge from global symmetries? In particular, examples that do not involve the introduction of new fields? I know that in string theory global symmetries of the world-sheet become local symmetries of space-time.