Modular Invariance, Soft Breaking, $\mu$ and $\tan\beta$ in Superstring   Models
  We go beyond parameterizations of soft terms in superstring models and investigate the dynamical assumptions that lead to the relative strength of the dilaton {\it vs} the moduli contributions in the soft breaking. Specifically, we discuss in some simple heterotic orbifold models sufficient conditions to achieve dilaton dominance. Assuming self-dual points to be minima we find multiple solutions to the trilinear and bilinear soft parameters $A_0$ and $B_0$. We discuss the constraints on $\mu$ and $\tan\beta$ in superstring models in the context of radiative breaking of the electroweak symmetry. We show that string models prefer a small to a moderate value of $\tan\beta$, {\it i.e}. $\tan\beta \leq 10$, and a value much larger than this requires a high degree of fine tuning. Further, we show that for large $\tan\beta$ the radiative electroweak symmetry breaking constraint leads to a value $\alpha_{string}=g_{string}^2/4\pi$ which is typically an order of magnitude smaller than implied by the LEP data and the heterotic superstring relation $g_{string}=k_ig_i$, where $g_i$ is the gauge coupling constant for the gauge group $G_i$ and $k_i$ is the corresponding Kac-Moody level in the class of models considered. This situation can be overcome by another fine tuned cancellation between the dilaton and the moduli contributions in the soft parameters. 
Pran Nath and Tomasz R. Taylor