Noncommutative Dirac–Born–Infeld action for D-brane

Abstract

We derive the noncommutative Dirac–Born–Infeld action for the D-brane, which governs dynamics of D-brane with a NS-NS B-field in the low energy regime. Depending on some details of the path integral prescriptions, both ordinary Dirac–Born–Infeld action and noncommutative one can be obtained by evaluating the same Polyakov string path integral for the open string ending on the D-brane. Thus, it establishes the equivalence of the noncommutative Dirac–Born–Infeld action and the ordinary one.