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The Goldstone scalars form the coordinates of a geometric space, a Kahler manifold. For the nonsupersymmetric case, the metric of this Kahler manifold is unique, and it uniquely determines the sigma-model lagrangian. But for the supersymmetric case, the quasi Goldstones double the coordinates of the geometry, and away from the "Goldstone hyperplane" the metric - and consequently the lagrangian - is no longer unique.

These sigma models are effective theories. The parts of the sigma-model lagrangian that are not determined by the coset geometry, are determined by details of the deeper theory that has undergone spontaneous symmetry breaking. For example, suppose we had a brane stack in a compactification, with some strongly coupled supersymmetric theory as its worldvolume theory. The basic properties of the brane stack may imply a particular coset sigma model as effective theory, while the geometric details of the compactification may determine the details of the lagrangian.

In terms of the sbootstrap, one could then proceed as follows. Identify a sbootstrap supersymmetric sigma model, such that the SM fermions are its goldstone fermions; and perhaps a specific potential for the fermion masses. Then find a brane configuration which implements that sigma model, and a compactification geometry which induces the desired potential. This 2016 paper offers a small start by considering possible supersymmetric mass terms for pions.