Topological DBI actions and nonlinear instantons

TL;DR

This paper develops topological DBI actions for Euclidean D4 and D6-branes with background B-fields, expressing them as squares of nonlinear instanton equations to facilitate supersymmetrization.

Contribution

It introduces a novel formulation of D-brane actions as squares of nonlinear instanton equations, enabling supersymmetrization via topological field theory methods.

Findings

Actions are equivalent to DBI actions up to total derivatives.

Actions can be written as squares of nonlinear instanton equations.

Facilitates supersymmetrization of D-brane actions.

Abstract

We consider Euclidean D4 and D6-branes filling the whole ${\bf R}^4$ and ${\bf R}^6$ space, respectively. In both cases, with a constant background B-field turned on for D4-branes, we propose actions which are the same as the DBI actions up to some constant or total derivative terms. These extra terms allow us to write the action as a square of nonlinear instanton equations. As such, the actions can easily be supersymmetrized using the methods of topological field theory.