2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105959A 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.4 pages with two columns; comments and references added, to appear in Phys. Rev. LettHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext