D-branes in Generalized Geometry and Dirac-Born-Infeld Action

TL;DR

This paper reformulates the Dirac-Born-Infeld action within generalized geometry, revealing its symmetry properties and interpreting scalar and gauge fields as generalized Nambu-Goldstone bosons, thus advancing the geometric understanding of D-branes.

Contribution

It introduces a generalized geometric framework for the DBI action, unifying scalar and gauge fields and clarifying symmetry transformations.

Findings

DBI action is invariant under generalized diffeomorphisms and B-field gauge transformations.

Scalar and gauge fields on D-branes are interpreted as generalized Nambu-Goldstone bosons.

The framework clarifies the symmetry structure of D-branes in generalized geometry.

Abstract

The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action in a framework of generalized geometry and clarify its symmetry. A D-brane is defined as a Dirac structure where scalar fields and gauge field are treated on an equal footing in a static gauge. We derive generalized Lie derivatives corresponding to the diffeomorphism and B-field gauge transformations and show that the DBI action is invariant under non-linearly realized symmetries for all types of diffeomorphisms and B-field gauge transformations. Consequently, we can interpret not only the scalar field but also the gauge field on the D-brane as the generalized Nambu-Goldstone boson.