Topological DBI actions and nonlinear instantons

We consider Euclidean D4 and D6-branes filling the whole R4 and R6 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.