Non-commutative world-volume interactions on D-brane and Dirac–Born–Infeld action Original Research Article

By integrating the Seiberg–Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterparts up to three non-commutative gauge fields. We then use this change of variables to write the ordinary abelian Dirac–Born–Infeld action in terms of non-commutative fields. The resulting action is then compared with various low-energy contact terms of world-sheet perturbative string scattering amplitudes from a non-commutative D p -brane. We find complete agreement between the field theory and string theory results. Hence, it shows that perturbative string theory knows the solution of the Seiberg–Witten differential equation.