  We begin the study of a class of string-motivated effective supergravity
theories in light of current data from the CERN Large Hadron Collider (LHC).
The case of heterotic string theory, in which the dilaton is stabilized via
non-perturbative corrections to the Kahler metric, will be considered first.
This model is highly constrained and therefore predictive. We find that much of
the reasonable parameter space afforded to the model -- representing the strong
dynamics of a presumed gaugino condensation in the hidden sector -- is now
observationally disfavored by the LHC results. Most of the
theoretically-motivated parameter space that remains can be probed with data
that has already been collected, and most of the remainder will be definitively
explored within the first year of operation at center of mass energy of 13 TeV.
Expected signatures for a number of benchmark points are discussed. We find
that the surviving space of the model makes a precise prediction as to the
relation of many superpartner masses, as well as the manner in which the
correct dark matter relic density is obtained. Implications for current and
future dark matter search experiments are discussed.
