We summarize recent work in which we attempt to make a consistent model of LHC physics, from the Pyramid Scheme. The models share much with the NMSSM, in particular, enhanced tree level contributions to the Higgs mass and a preference for small tan {
beta}. There are 3 different singlet fields, and a new strongly coupled gauge theory, so the constraints of perturbative unification are quite different. We outline our general approach to the model, which contains a Kahler potential for three of the low energy fields, which is hard to calculate. Detailed calculations, based on approximations to the Kahler potential, will be presented in a future publication.
We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $Z_p$ gauge theories shows that they are associated with an emergent $Z_p$ o
ne-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear $sigma$-models. It also allows us to expand on Polchinskis classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.
We discuss SUSY models in which renormalizable lepton number violating couplings hide the decay of the Higgs through h -> chi_1^0 + chi_1^0 followed by chi_1^0 -> tau + 2 jets or chi_1^0 -> u_tau + 2 jets and also explain neutrino masses. This mecha
nism can be made compatible with gauge mediated SUSY breaking.
