Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson lines

We write the recently conjectured action for transformation of the ordinary Born-Infeld action under the Seiberg-Witten map with one open Wilson conto ur in a manifestly noncommutative gauge invariant form. This action contain s the nonconstant closed string fields, higher order derivatives of the non commutative gauge fields through the *(N)-product, and a Wilson operator. W e extend this noncommutative D-9-brane action to the action for D-p-brane b y transforming it under T-duality. Using this noncommutative Dp-brane actio n 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. (C) 2001 Published by El sevier Science B.V.