  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.
