Gravitational Instantons from Gauge Theory

Abstract

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.

4 pages with two columns; comments and references added, to appear in Phys. Rev. Lett

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