Abstract :
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 background 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 must 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 ∗ and the ∗N product is just some total 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 transforming the ordinary Dirac–Born–Infeld action (including the closed string fields) under the Seiberg–Witten map. We then conjecture a non-commutative DBI action for the transformation of the commutative DBI action under the SW map.
