Noncommutative Dirac-Born-Infeld Action for D-brane

TL;DR

This paper derives the noncommutative Dirac-Born-Infeld action for D-branes with a B-field, showing its equivalence to the ordinary action through string path integral methods, advancing understanding of D-brane dynamics.

Contribution

It establishes the derivation of the noncommutative Dirac-Born-Infeld action from string theory and demonstrates its equivalence to the ordinary action.

Findings

Derived the noncommutative D-brane action from string theory.

Showed the equivalence between noncommutative and ordinary Dirac-Born-Infeld actions.

Connected path integral prescriptions to different forms of the D-brane action.

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.