Dirac–Born–Infeld action, Seiberg–Witten map, and Wilson lines Original Research Article

We write the recently conjectured action for transformation of the ordinary Born–Infeld action under the Seiberg–Witten map with one open Wilson contour in a manifestly noncommutative gauge invariant form. This action contains the nonconstant closed string fields, higher order derivatives of the noncommutative gauge fields through the ∗N-product, and a Wilson operator. We extend this noncommutative D9-brane action to the action for Dp-brane by transforming it under T-duality. Using this noncommutative Dp-brane action we then evaluate the linear couplings of the graviton and dilaton to the brane for arbitrary noncommutative parameters. By taking the Seiberg–Witten limit we show that they reduce exactly to the known results of the energy–momentum tensor of the noncommutative super-Yang–Mills theory. We take this as an evidence that the noncommutative action in the Seiberg–Witten limit includes properly all derivative correction terms.