GUT and Supersymmetry at the LHC and in dark matter
  Conventional SO(10) models involve more than one scale for a complete breaking of the GUT symmetry requiring further assumptions on the VEVs of the Higgs fields that enter in the breaking to achieve viable models. Recent works where the breaking can be accomplished at one scale are discussed. These include models with just a pair of $144+\bar{144}$ of Higgs fields. Further extensions of this idea utilizing $560+ \bar{560}$ of Higgs representations allow both the breaking at one scale, as well as accomplish a natural doublet-triplet splitting via the missing partner mechanism. More generally, we discuss the connection of high scale models to low energy physics in the context of supergravity grand unification. Here we discuss a natural solution to the little hierarchy problem and also discuss the implications of the LHC data for supersymmetry. It is shown that the LHC data implies that most of the parameter space of supergravity models consistent with the data lie on the Hyperbolic Branch of radiative breaking of the electroweak symmetry and more specifically on the Focal Surface of the Hyperbolic Branch. A discussion is also given of the implications of recent LHC data on the Higgs boson mass for the discovery of supersymmetry and for the search for dark matter. 
Pran Nath
hep-ph astro-ph.HE