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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.
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