D-Brane Actions, Intrinsic Geometry and Duality

TL;DR

The paper introduces a new quadratic form of the supersymmetric D-p-brane action involving an auxiliary tensor, enabling duality transformations that replace gauge fields with higher-form fields, simplifying the analysis of brane dynamics.

Contribution

It presents an alternative, simplified form of the D-brane action using an auxiliary tensor, facilitating duality transformations and generalizing previous formulations.

Findings

Derived a quadratic D-brane action with an auxiliary tensor.

Showed how to perform duality transformations to replace gauge fields.

Recovered known dual D-2-brane action as an example.

Abstract

We discuss an alternative form of the supersymmetric D-$p$-brane action which is quadratic in derivatives of $X$ and linear in $F_{\mu \nu}$. This action involves an auxiliary worldvolume tensor and generalises the simplification of the Nambu-Goto action for $p$-branes using a symmetric metric. When the worldvolume gauge field is abelian, it appears as a Lagrange multiplier, and solving the constraint gives the dual form of the ($p+1$)-dimensional action with a $p-2$ form gauge field instead of a vector gauge field. This is illustrated by the example of the dual D-2-brane action, for which the known result is recovered.