Charge quantization in the CP(1) nonlinear σ-model

We investigate the consistency conditions for matter fields coupled to the four-dimensional ( N = 1 supersymmetric) C P ( 1 ) nonlinear sigma model (the coset space SU ( 2 ) G / U ( 1 ) H ). We find that consistency requires that the U ( 1 ) H charge of the matter be quantized, in units of half of the U ( 1 ) H charge of the Nambu–Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group SU ( 2 ) G . We can then take the linearly realized group U ( 1 ) H to comprise the weak hypercharge group U ( 1 ) Y of the Standard Model. Thus we have charge quantization without a Grand Unified Theory (GUT), completely avoiding problems like proton decay, doublet–triplet splitting, and magnetic monopoles. We briefly investigate the phenomenological implications of this model-building framework. The NG boson is fractionally charged and completely stable. It can be naturally light, avoiding constraints while being a component of dark matter or having applications in nuclear physics. We also comment on the extension to other NLSMs on coset spaces, which will be explored more fully in a followup paper.