N=2 and N=4 supersymmetric Born-Infeld theories from nonlinear realizations

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 objects are the bosonic Goldstone N = 2 and N =4 superfields associated with the central charge generators. By construction, the equations are manifestly N = 2 and N = 4 supersymmetric and enjoy covariance under another nonlinearly realized half of the original supersymmetries. They provide a manifestly 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 restore, up to the sixth order, the off-shell N = 2 Born-Infeld action with the second hidden N = 2 supersymmetry. (C) 2001 Published by Elsevier Science B.V.