 Thus far, we have been discussing symmetries which act on the space of states of a physical theory. In recent years, much discussion within physics and philosophy has centered on certain kinds of symmetries that act on the space of theories. When such symmetries are interpreted as realizing an “equivalence” (which sense is itself something that requires philosophical work to explicate) between two theories, the theories are typically said to be related by a “duality symmetry” (and if we are speaking of “symmetry” in the strict sense of an automorphism, then such dualities are called “self-dualities”). 