Born-Infeld-Goldstone superfield actions for gauge-fixed D5- and D3-branes in 6d

The supersymmetric Born-Infeld actions describing gauge-fixed D-5- and D3-branes in ambient six-dimensional (6d) space-time 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.