The supersymmetric Born-Infeld actions describing gauge-fixed D-5- and
D-3-branes in ambient six-dimensional (6d) spacetime are constructed in
superspace. A new 6d action is the (1,0) supersymmetric extension of the 6d
Born-Infeld action. It is related via dimensional reduction to another
remarkable 4d action describing the N=2 supersymmetric extension of the
Born-Infeld-Nambu-Goto action with two real scalars. Both actions are the
Goldstone actions associated with partial (1/2) spontaneous breaking of
extended supersymmetry having 16 supercharges down to 8 supercharges. Both
actions can be put into the `non-linear sigma-model' form by using certain
non-linear superfield constraints. The unbroken supersymmetry is always
linearly realised in our construction.Comment: 39 pages, LaTeX; a few style and sign corrections, a reference adde