Non-commutative world-volume interactions on D-brane and Dirac-Born-Infeldaction

By integrating the Seiberg-Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterpar ts up to three non-commutative gauge fields. We then use this change of var iables to write the ordinary abelian Dirac-Born-Infeld action in terms of n on-commutative fields. The resulting action is then compared with various l ow-energy contact terms of world-sheet perturbative string scattering ampli tudes from a non-commutative Dp-brane. We find complete agreement between t he field theory and string theory results. Hence, it shows that perturbativ e string theory knows the solution of the Seiberg-Witten differential equat ion. (C) 2000 Elsevier Science B.V. All rights reserved.