Coset approach to the partial breaking of global supersymmetry

Abstract: We propose a method to construct on-shell component actions for theories with 1/2 partial breaking of global supersymmetry within the nonlinear realization (coset) approach. In contrast with the standard superfield approach in which unbroken supersymmetry plays the leading role, we have shifted the attention to the spontaneously broken supersymmetry. It turns out that in theories in which half of supersymmetries is spontaneously broken, all physical fermions are just the fermions of the nonlinear realization. Moreover, transformation properties of these fermions with respect to broken supersymmetry are the same as in the Volkov-Akulov model. Just this completely fixed all possible appearances of fermions in the component action: they can enter the action through the determinant of the vielbein and covariant derivatives, only. In our parametrization of the coset the rest of physical components, i.e. all bosonic components, transform as "matter fields" with respect to broken supersymmetry. Clearly, the component action acquires the form of the Volkov-Akulov action for these "matter fields". The complete form of the action can be further fixed by two additional requirements: a) to reproduce the bosonic limit, which is explicitly known in many interesting cases, and b) to have a proper linearized form, which has to be invariant with respect to linearized unbroken supersymmetry. In some cases additional Wess-Zumino terms (which disappear in the bosonic limit) have to be added to the action. We supply the general consideration by detailed examples of actions for the superparticle in D=3,5, the on-shell component action for N=1, D=5 supermembrane and its dual cousins and the component action of N=1 supermembrane in D=4, providing the exact proof of the invariance of the constructed component actions with respect to both broken and unbroken supersymmetries.