A fugue state
describes a state of mind where a person experiences a break in identity and attempts to run away from some perceived threat, usually something abstract such as the person's identity. It is often triggered by stress.
People who enter into a fugue state may disappear, running away to a completely different geographical region and assuming another identity.
Also called a "fugue state" by non-psychologists is the state of mind attained by a gifted pianist or athlete where the person attains a high degree of focus and attention to their art or actions. This is also a dissociation from one's surroundings, to concentrate on the work at hand.