On the Dirac-Born-Infeld Action for D-branes

TL;DR

This paper reformulates the Dirac-Born-Infeld action for D-branes using a Brink-Di Vecchia-Howe-Tucker approach, deriving explicit expressions for specific cases and discussing supersymmetrization.

Contribution

It introduces a new reformulation of the DBI action with an independent metric and derives explicit forms for p=3 and p=4, advancing theoretical understanding of D-brane dynamics.

Findings

Derived a closed form for p=3 DBI action.

Reproduced the DBI action for selfdual field strengths with a simple F^2 term.

Provided governing equations and implicit expressions for arbitrary p.

Abstract

In this note, we consider the reformulation of the Dirac-Born-Infeld action for a Dirichlet p-brane in Brink-Di Vecchia-Howe-Tucker form, i.e., including an independent non-propagating world-volume metric. When p>2, the action becomes non-polynomial. A closed expression is derived for p=3. For selfdual field-strengths, the DBI action is reproduced by an action with a simple F^2 term. We speculate on supersymmetrization of the D_3-brane action. We also give the governing equations for arbitrary p, and derive an implicit expression for the D_4-brane lagrangian.