Partial breaking of global D=4 supersymmetry, constrained superfields,   and 3-brane actions
  We show that the connection between partial breaking of supersymmetry and nonlinear actions is not accidental and has to do with constraints that lead directly to nonlinear actions of the Born-Infeld type. We develop a constrained superfield approach that gives a universal way of deriving and using these actions. In particular, we find the manifestly supersymmetric form of the action of the 3-brane in 6-dimensional space in terms of N=1 superfields by using the tensor multiplet as a tool. We explain the relation between the Born-Infeld action and the model of partial N=2 supersymmetry breaking by a dual D-term. We represent the Born-Infeld action in a novel form quadratic in the gauge field strengths by introducing two auxiliary complex scalar fields; this makes duality covariance and the connection with the N=1 supersymmetric extension of the action very transparent. We also suggest a general procedure for deriving manifestly duality symmetric actions, explaining in a systematic way relations between previously discussed Lorentz covariant and noncovariant actions. 
M. Rocek and A.A. Tseytlin