Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-05-15
Nucl.Phys. B611 (2001) 467-487
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, Latex, revised some parts in such a way that not to be concluded that the proposed non-commutative action is identic
Scientific paper
10.1016/S0550-3213(01)00355-8
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 non-commutative gauge invariant form. This action contains the non-constant closed string fields, higher order derivatives of the non-commutative gauge fields through the $*_N$-product, and a Wilson operator. We extend this non-commutative $D_9$-brane action to the action for $D_p$-brane by transforming it under T-duality. Using this non-commutative $D_p$-brane action we then evaluate the linear couplings of the graviton and dilaton to the brane for arbitrary non-commutative parameters. By taking the Seiberg-Witten limit we show that they reduce exactly to the known results of the energy-momentum tensor of the non-commutative super Yang-Mills theory. We take this as an evidence that the non-commutative action in the Seiberg-Witten limit includes properly all derivative correction terms.
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