No abstract

We discuss supersymmetry breakdown in effective supergravities such as emerge in the lowenergy limit of superstring theory. Without specifying the precise trigger of the breakdown, we analyse the soft parameters in the Lagrangian of the supersymmetrized Standard Model.

As originally published, the article contained a few minor errors. Unfortunately, these errors have lately caused a not-so-minor confusion among several physicists working on the phenomenology of string unification. To avoid further confusion, I would like to make the following corrections:

We study the low-energy effective Lagrangian of N = 2 heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional N = 1 supersymmetric vacua.

Classical vacua of the heterotic string corresponding to c = 9, N = (2,2) superconformal theories on the world sheet yield low-energy effective field theories with N = 1 space-time supersymmetry in four dimensions, gauge group EC @ Es, several families of 27 and 27 matter fields, and moduli fields. String theory relates matter fields to moduli; in this article we relate the kinetic terms in the effective Lagrangian for both moduli and matter fields to the 273 and z3 Yukawa couplings.Geometrically, we recover the result (obtained previously via the type II superstring and N = 2 supergravity) that moduli space is a direct product of two Mahler manifolds of restricted type, spanned by the moduli related respectively to the 27 and 27 matter fields. The holomorphic functions of the moduli genera,ting the' two restricted Kahler metrics also determine the Yukawa couplings of the matter fields. We derive explicit formulaa for the metric for the matter fields in terms of the metric for the corresponding moduli; the two metrics are not identical to each other.The precise relation between moduli and matter metrics takes a slightly different form on subspaces of the moduli space where the unbroken gauge symmetry is enhanced beyond Es @ E8 ; this phenomenon is illustrated using the examples of (2,2) orbifolds and tensor products of minimal N = 2 theories.