Space-filling D3-brane within coset approach

We derive the component on-shell action of the space-filling D3-brane, {\it i.e.} $N=1$ supersymmetric Born-Infeld action, within the nonlinear realization approach. The covariant Bianchi identity defining the $N=1$, $d=4$ vector supermultiplet has been constructed by introducing a new bosonic Goldstone superfield associated with the generator of the $U(1)$ group, which transforms to each other the spinor generators of unbroken and spontaneously broken $N=1$, $d=4$ supersymmetries. The first component of this Goldstone superfield is the auxiliary field of the vector supermultiplet and, therefore, the Bianchi identity can be properly defined. The component action of the D3-brane has a very simple form, being written in terms of derivatives covariant with respect to spontaneously broken supersymmetry - it just mimics its bosonic counterpart.