Supersymmetry breaking and Fermi balls.

The possibility exists that the early universe experienced a sequence of symmetry breaking phase transitions, which could have resulted in the production of defects, such as monopoles, cosmic strings, or domain walls [1–3]. Furthermore, it is possible that supersymmetry could have been physically realized during early epochs, becoming broken after defect formation, at a lower energy scale. It is therefore quite natural to investigate models of defects within a supersymmetric context. Here, attention is focused upon a simple supersymmetric model constructed from a single chiral supermultiplet, which admits a domain wall solution interpolating between two distinct, but energetically degenerate, supersymmetric vacuum states. The domain wall formation arises from an exact discrete symmetry which is spontaneously broken. The initial supersymmetry of the model couples the fermion fields to the scalar fields in a prescribed way, and it is found that, as a result of this coupling, a fermion zero mode [4] forms within the core of the domain wall, where the fermion is essentially massless. Bound states can also exist which describe scalar bosons attached to the wall. The breaking of supersymmetry at lower energies can be described by the inclusion of soft supersymmetry breaking terms in the scalar potential. However, it is found that when the soft supersymmetry breaking terms are added to the Lagrangian, the exact discrete symmetry responsible for the formation of the stable domain wall is transformed into an approximate, or biased, discrete symmetry. This approximate discrete symmetry results in a domain wall network where each wall interpolates between two different, energetically nondegenerate (and nonsupersymmetric) vacuum