English

Charge Quantization in the $\mathbb{CP}(1)$ Nonlinear Sigma-Model

High Energy Physics - Theory 2013-12-17 v2 High Energy Physics - Phenomenology

Abstract

We investigate the consistency conditions for matter fields coupled to the four-dimensional (N=1{\cal N} = 1 supersymmetric) CP(1)\mathbb{CP}(1) nonlinear sigma model (the coset space SU(2)G/U(1)HSU(2)_G/U(1)_H). We find that consistency requires that the U(1)HU(1)_H charge of the matter be quantized, in units of half of the U(1)HU(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)GSU(2)_G. We can then take the linearly realized group U(1)HU(1)_H to comprise the weak hypercharge group U(1)YU(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.

Keywords

Cite

@article{arxiv.1309.0692,
  title  = {Charge Quantization in the $\mathbb{CP}(1)$ Nonlinear Sigma-Model},
  author = {Simeon Hellerman and John Kehayias and Tsutomu T. Yanagida},
  journal= {arXiv preprint arXiv:1309.0692},
  year   = {2013}
}

Comments

6 pages; v2 minor updates (anti-holomorphic details, typos), matches published version

R2 v1 2026-06-22T01:19:46.093Z