Narrow Results

Under a few mild assumptions, supersymmetry (SUSY) in four dimensions is shown to be spontaneously broken in a metastable vacuum in a self-consistent Hartree–Fock approximation of Bardeen–Cooper–Schrieffer/Nambu–Jona-Lasinio (BCS/NJL) type to the leading order, in the gauge theory specified by the gauge kinetic function and the superpotential of adjoint chiral superfields, in particular, that possess extended SUSY spontaneously broken to at tree level. We derive an explicit form of the gap equation, showing the existence of a nontrivial solution. The gauginos in the observable sector receive mixed Majorana–Dirac masses and are split due to both the nonvanishing 〈D⁰〉 and 〈F⁰〉 induced with 〈D⁰〉. It is argued that proper physical applications and assessment of the range of the validity of our framework are made possible by rendering the approximation into expansion.