Supersymmetry, naturalness, and dynamical supersymmetry breaking.

Abstract

Models with dynamical supersymmetry breaking have the potential to solve many of the naturalness problems of hidden sector supergravity models. We review the argument that in a generic supergravity theory in which supersymmetry is {\it dynamically} broken in the hidden sector, only tiny Majorana masses for gauginos are generated. This situation is similar to that of theories with continuous R-symmetries, for which Hall and Randall have suggested that gluino masses could arise through mixings with an octet of chiral fields. We note that in hidden sector models, such mixing can only occur if the auxiliary D field of a $U(1)$ gauge field has an expectation value. This in turn gives rise to a catastrophically large Fayet-Iliopoulos term for ordinary hypercharge. To solve this problem it is necessary to unify hypercharge at least partially in a non-Abelian group. We consider, also, some general issues in models with continuous or discrete R symmetries, noting that it may be necessary to include $SU(2)$ triplet fields, and that these are subject to various constraints. In the course of these discussions, we consider a number of naturalness problems. We suggest that the so-called ``$\mu$-problem" is not a problem, and point out that in models in which the axion decay constant is directly related to the SUSY breaking scale, squarks, sleptons and Higgs particles generically acquire huge masses.