Intrinsic Geometry of D-Branes

TL;DR

This paper reformulates D-brane actions using an auxiliary metric with symmetric and anti-symmetric parts, simplifying their structure and deriving dual forms, including supersymmetric extensions.

Contribution

Introduces a new formulation of D-brane actions with an auxiliary metric, enabling explicit dual actions and extending to supersymmetric cases.

Findings

Derived quadratic derivative forms of Born-Infeld and D-brane actions.

Explicitly constructed dual actions with higher-form gauge fields.

Extended formulation to supersymmetric D-brane actions.

Abstract

We obtain forms of Born-Infeld and D-brane actions that are quadratic in derivatives of $X$ and linear in $F_{\mu \nu}$ by introducing an auxiliary `metric' which has both symmetric and anti-symmetric parts, generalising the simplification of the Nambu-Goto action for $p$-branes using a symmetric metric. The abelian gauge field appears as a Lagrange multiplier, and solving the constraint gives the dual form of the $n$ dimensional action with an $n-3$ form gauge field instead of a vector gauge field. We construct the dual action explicitly, including cases which could not be covered previously. The generalisation to supersymmetric D-brane actions with local fermionic symmetry is also discussed.