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We propose a systematic way of constructing $N=2, d=4$ superfield Born-Infeldaction with a second nonlinearly realized N=2 supersymmetry. The latter,together with the manifest N=2 supersymmetry, form a central-charge extended$N=4, d=4$ supersymmetry. We embed the Goldstone-Maxwell N=2 multiplet into aninfinite-dimensional off-shell supermultiplet of this N=4 supersymmetry andimpose an infinite set of covariant constraints which eliminate all extra N=2superfields through the Goldstone-Maxwell one. The Born-Infeld superfieldLagrangian density is one of these composite superfields. The constraints canbe solved by iterations to any order in the fields. We present the sought N=2Born-Infeld action up to the 10th order. It encompasses the action foundearlier by Kuzenko and Theisen to the 8th order from a self-dualityrequirement. This is a strong indication that the complete N=2 Born-Infeldaction with partially broken N=4 supersymmetry is also self-dual.Comment: 12 pages, LaTeX, typos corrected, version to appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Towards the complete<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>superfield Born-Infeld action with partially broken<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mn /></mml:math>supersymmetry

Towards the completeN=2superfield Born-Infeld action with partially brokenN=4supersymmetry