Low-mass solitons from fractional charges in quantum chromodynamics

Abstract

Slansky, Goldman, and Shaw have proposed a model to account for the observation of fractionally charged states. We show that in this model, there are expected to be several low-mass solitons (four being in the mass range \ensuremath{\sim}20-60 MeV) associated with the third homotopy group ${\ensuremath{\pi}}_{3}(\frac{\mathrm{SU}(3)}{\mathrm{SO}(3)})={Z}_{4}$, besides a low-mass (\ensuremath{\sim}30 MeV) ${\mathrm{Z}}_{2}$ monopole. Confirmation of these levels and hence of the model has important implications for Cabrera's results on the magnetic monopole. An efficient algorithm for the calculation of ${\ensuremath{\pi}}_{3}(\frac{G}{H})$ for a general Lie group $G$ and a subgroup $H$ is developed. It is pointed out that solitons associated with the third homotopy group are predicted by some grand-unified-theory scenarios.