Nonlinear superfield realisations of extended supersymmetries

A superfield extension of the Volkov-Akulov method [1974 Theor. Math. Phys. 18,28] of constructing nonlinear realisations of the extended super Poincare symmetry is proposed. The formalism describes a partial supersymmetry breaking, the N=1 supersymmetry remaining unbroken. The case N=2, spontaneously broken down to N=1, is considered in detail. It is shown that in the quadratic approximation the corresponding action contains ghost fields in accordance with the general discussion of supersymmetry breaking. Finally, a nonlinear superfield realisation of N=2 Poincare supersymmetry is considered with three scalar Goldstone superfields describing the U(2)/U(1) sector of the internal symmetry. (author)