Transformation of the Dirac-Born-Infeld action under the Seiberg-Witten map

We explicitly evaluate the disk S-matrix elements of one closed string and an arbitrary number of open string states in the presence of a large backgr ound B-flux, From this calculation, we show that in the world-volume action of D-branes in terms of non-commutative fields, the closed string fields m ust be treated as functionals of the non-commutative gauge fields. We also find the generalized multiplication rule *N between N open string fields on the world-volume of the D-brane, In particular, this result indicates that the difference between the familiar x and the *N product is just some tota l derivative terms, We show that the *N product. and the dependence of the closed string fields on the non-commutative gauge fields emerge also from t ransforming the ordinary Dirac-Born-Infeld action (including the closed str ing fields) under the Seiberg-Witten map. We then conjecture a non-commutat ive DBI action for the transformation of the commutative DBI action under t he SW map. (C) 2001 published by Elsevier Science B.V.