  A gauge theory can be formulated on a noncommutative (NC) spacetime. This NC
gauge theory has an equivalent dual description through the so-called
Seiberg-Witten (SW) map in terms of an ordinary gauge theory on a commutative
spacetime. We show that all NC U(1) instantons of Nekrasov-Schwarz type are
mapped to ALE gravitational instantons by the exact SW map and that the NC
gauge theory of U(1) instantons is equivalent to the theory of hyper-Kaehler
geometries. It implies the remarkable consequence that ALE gravitational
instantons can emerge from local condensates of purely NC photons.
