Adding a Brane to the Brane-Anti-Brane Action in BSFT

We attempt to generalize the effective action for the D-brane-anti-D-brane system obtained from boundary superstring field theory (BSFT) by adding an extra D-brane to it to obtain a covariantized action for 2 D-branes and 1 anti-D-brane. We discuss the approximations made to obtain the effective action in closed form. Among other properties, this effective action admits solitonic solutions of codimension 2 (vortices) when one of the D-brane is far separated from the brane-anti-brane pair.