Dark Matter and Electroweak Symmetry Breaking from $SO(10)$
  We consider a minimal model of GUT scalar dark matter (DM) stabilized by the
discrete gauge matter parity $P_{X}$ that arises from breaking of $SO(10)$. The
dark sector comprises the complex singlet $S$ and the inert doublet $H_{2}$.
GUT scale parameters are evaluated to the electroweak scale via Renormalization
Group Equations (RGEs). Experimental and theoretical constraints limit the DM
mass to the 80 GeV to 2 TeV range. The EW symmetry breaking is radiative and
can occur via RGE running and 1-loop matching corrections from integrating out
DM. Because the next-to-lightest scalar is almost degenerate with DM, it gives
a background free displaced decay vertex at the LHC.
