Starting from nonlinear realizations of the partially broken central-charge
extended N = 4 and N = 8 Poincare supersymmetries in D = 4, we derive the
superfield equations of N = 2 and N = 4 Born-Infeld theories. The basic obj
ects are the bosonic Goldstone N = 2 and N =4 superfields associated with t
he central charge generators. By construction, the equations are manifestly
N = 2 and N = 4 supersymmetric and enjoy covariance under another nonlinea
rly realized half of the original supersymmetries. They provide a manifestl
y worldvolume supersymmetric static-gauge description of D3-branes in D = 6
and D = 10. For the N = 2 case we find, to lowest orders, the equivalence
transformation to the standard N = 2 Maxwell superfield strength and restor
e, up to the sixth order, the off-shell N = 2 Born-Infeld action with the s
econd hidden N = 2 supersymmetry. (C) 2001 Published by Elsevier Science B.
V.