Dimensional Reduction of the Generalized DBI

TL;DR

This paper investigates the dimensional reduction of the generalized Dirac-Born-Infeld (DBI) action, exploring its descriptions in different settings and extending the theory with additional gauge potentials.

Contribution

It provides a detailed analysis of the dimensional reduction of the generalized DBI action and extends the theory to include a one-form gauge potential.

Findings

Dimensional reduction yields the standard DBI theory for q=2.

The generalized DBI action can be described in both commutative and non-commutative frameworks.

Extension includes incorporating a one-form gauge potential.

Abstract

We study the generalized Dirac-Born-Infeld (DBI) action, which describes a $q$-brane ending on a $p$-brane with a ($q$+1)-form background. This action has the equivalent descriptions in commutative and non-commutative settings, which can be shown from the generalized metric and Nambu-Sigma model. We mainly discuss the dimensional reduction of the generalized DBI at the massless level on the flat spacetime and constant antisymmetric background in the case of flat spacetime, constant antisymmetric background and the gauge potential vanishes for all time-like components. In the case of $q=2$, we can do the dimensional reduction to get the DBI theory. We also try to extend this theory by including a one-form gauge potential.