A manifestly N = 2 supersymmetric Born-Infeld action

A manifestly N = 2 supersymmetric completion of the four-dimensional Nambu-Goto-Born-Infeld action, which is self-dual with respect to electric-magnetic duality, is constructed in terms of an Abelian N = 2 superfield strength W in the conventional N = 2 superspace. A relation to the known N = 1 supersymmetric Born-Infeld action in N = 1 superspace is established. The action found can be considered either as the Goldstone action associated with a partial breaking of N = 4 supersymmetry down to N = 2, with the N = 2 vector superfield being a Goldstone field, or, equivalently, as the gauge-fixed superfield action of a (D - 3)-brane in flat six-dimensional ambient space-time.