High Energy Physics

I will first summarize recent exact localization computations of supersymmetric gauge theories, and then discuss curious connections between SUSY/non-SUSY theories coming from 6d (2,0) theories. I particular, I will focus on our recent proposal relating 3d N=2 theories and 3d SL(2,R) Chern-Simons theories (or more mathematically, geometry of 3-manifolds).

The hierarchy of the Yukawa couplings is an outstanding problem of the standard model. We present a class of models in which the first and second generation fermions are SUSY partners of pseudo-Nambu-Goldstone bosons that parameterize an E_7/SO(10) Kahler manifold, explaining the small values of these fermion masses relative to those of the third generation. We consider experimental constraints on this scenario, and find that the simplest model with universal gaugino masses is already ruled out by the LHC. However, models with non-universal gaugino masses will likely be excluded only by direct dark matter searches.

The observed conservation of Baryon and Lepton number may arise because they are gauge symmetries. Models are discussed where Baryon and lepton number are the charges for a spontaneously broken U(1) gauge symmetries. The best of these models is: (1) free of Landau poles that are near the weak scale, (2) has no flavor changing neutral currents at tree level and (3) contains a dark matter candidate.