D-term Dynamical SUSY Breaking

We consider an N=1 supersymmetric U(N) gauge theory with an adjoint chiral multiplet. By developing a self-consistent Hartree-Fock approximation to the leading order which is reminiscent of that of the BCS/NJL in the superconductivity/chiral symmetry, we show that the N=1 supersymmetry is spontaneously broken, giving a mixed Majorana-Dirac mass term for gaugino due to the nonvanishing D-term VEV and F-term one induced by D-term.