Modular Invariant Soft Breaking, WMAP, Dark Matter and Sparticle Mass   Limits
  An analysis of soft breaking under the constraint of modular invariance is given. The role of dilaton and moduli dependent front factors in achieving a modular invariant $V_{soft}$ is emphasized. Further, it is shown that in string models $\tan\beta$ is no longer a free parameter but is determined in terms of $\alpha_{string}$ and the other soft parameters by the constraints of modular invariance and radiative electroweak symmetry breaking. The above framework is then used to analyze the neutralino relic density consistent with the WMAP data at self dual points in the Kahler and complex structure moduli. One finds that the combined set of constraints arising from modular invariant soft breaking, radiative electroweak symmetry breaking and WMAP lead to upper limits on sparticle masses for $\mu>0$. These limits are investigated for a class of models and found to lie within reach of the Tevatron and of the Large Hadron Collider (LHC). Further, an analysis of the neutralino-proton cross section shows that dark matter in these models can be explored in CDMS (Soudan), GENIUS and ZEPLIN. While the analysis is carried out within the general framework of heterotic strings, the possibility that the results of the analysis may extend to a broader class of string models, such as models based on intersecting D branes, is also discussed. 
Utpal Chattopadhyay and Pran Nath