D-term Triggered Dynamical Supersymmetry Breaking

Abstract

We present the mechanism of the dynamical supersymmetry breaking at the metastable vacuum recently uncovered in the N=1 U(N) supersymmetric gauge theory that contains adjoint superfields and that is specified by Kahler and non-canonical gauge kinetic functions and a superpotential whose tree vacua preserve N=1 supersymmetry. The overall U(1) serves as the hidden sector and no messenger superfield is required. The dynamical supersymmetry breaking is triggered by the non-vanishing D term coupled to the observable sector, and is realized by the self-consistent Hartree-Fock approximation of the NJL type while it eventually brings us the non-vanishing F term as well. It is shown that theoretical analysis is resolved as a variational problem of the effective potential for three kinds of background fields, namely, the complex scalar, and the two order parameters D and F of supersymmetry, the last one being treated perturbatively. We determine the stationary point and numerically check the consistency of such treatment as well as the local stability of the scalar potential. The coupling to the N = 1 supergravity is given and the gravitino mass formula is derived.