This talk will give an overview of some new results on an old topic we are all familiar with: the good ol’ nonlinear sigma model (NLSM). The structure (as a group or topology) of the nonlinearly realized symmetry leads to charge quantization of a U(1) (i.e. hypercharge) without a monopole or Grand Unified Theory. We can extend this result to larger groups and find relations between the quantum numbers and a nontrivial quantization condition (e.g. relating charge and SU(2) representations). There is rich phenomenology and model building which can be done. Studying NLSMs in supergravity necessarily leads to flat directions and light fields. This is an ideal setting for models of high scale inflation, the Higgs, or an axion.
arXiv references: 1309.0692, 1312.6889, 1411.3720