Exact Seiberg-Witten map and induced gravity from noncommutativity

We find a closed form for Seiberg-Witten (SW) map between ordinary and noncommutative (NC) Dirac-Born-Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map lead to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field-dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles.