Matrix supermultiplet of N=2, D=4 supersymmetry and supersymmetric 3-brane

It is shown that the Lagrangian density of the supersymmetric 3-brane can be regarded as a component of an infinite-dimensional supermultiplet of N=2, D=4 supersymmetry spontaneously broken down to N=1. The latter is described by N=1 Hermitian bosonic matrix superfield Vmn=V†nm, [Vmn]=m+n, m,n=0,1,… in which the component V01 is identified with a chiral Goldstone N=1 multiplet associated with central charge of the N=2, D=4 superalgebra, and V11 obeys a specific nonlinear recursive equation providing the possibility to express V11 (as well as the other components Vmn) covariantly in terms of V01. We demonstrate that the solution of V11 gives the right PBGS action for the super-3-brane.