We discuss the results of a global 2 analysis of a simple SO10 supersymmetric grand unified theory (SUSY GUT) with D 3 family symmetry and low energy R parity. The model describes fermion mass matrices with 14 parameters and gives excellent fits to 20 observable masses and mixing angles in both quark and lepton sectors, giving six predictions. Bi-large neutrino mixing is obtained with hierarchical quark and lepton Yukawa matrices, thus avoiding the possibility of large lepton flavor violation. The model naturally predicts small 1-3 neutrino mixing, with sin 13 ' 0:05-0:06. In this paper we evaluate the predictions for the lepton flavor violating processes, ! e, ! and ! e and also the electric dipole moment of the electron (d e ), the muon, and the tau, assuming universal squark and slepton masses (m 16 ) and a universal soft SUSY breaking A parameter (A 0 ) at the GUT scale. We find Br ! e is naturally below present bounds, but may be observable by MEG. Similarly, d e is below present bounds, but it is within the range of future experiments. We also give predictions for the light Higgs mass (using FEYNHIGGS). We find an upper bound given by m h 127 GeV, with an estimated 3 GeV theoretical uncertainty. Finally we present predictions for SUSY particle masses in the favored region of parameter space.

We formulate N =1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-N c limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling g √ N c , and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for m 2 for some low energy bound states in the limit where the numerical resolution goes to infinity.

We consider the (1+1)-dimensional N = (2, 2) super Yang-Mills theory which is obtained by dimensionally reducing N = 1 super Yang-Mills theory in four dimension to two dimensions. We do our calculations in the large-N c approximation using Supersymmetric Discrete Light Cone Quantization. The objective is to calculate quantities that might be investigated by researchers using other numerical methods. We present a precision study of the low-mass spectrum and the stress-energy correlator T ++ (r)T ++ (0) . We find that the mass gap of this theory closes as the numerical resolution goes to infinity and that the correlator in the intermediate r region behaves like r −4.75 .

Species doubling is a problem that infects most numerical methods that use a spatial lattice. An understanding of species doubling can be found in the Nielsen-Ninomiya theorem which gives a set of conditions that require species doubling. The transverse lattice approach to solving field theories, which has at least one spatial lattice, fails one of the conditions of the Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the standard Lagrangian formulation of the transverse lattice. We will show that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the transverse lattice does not have species doubling.

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