  Optical trapping techniques allow for the formation of bosonic condensates
with internal degrees of freedom, so-called spinor condensates. Mean-field
models of spinor condensates highlight the sensitivity of the quantum phases of
the system to the relative strength of the two-body interaction in the
different spin-channels. Such a description captures the regime where these
interactions are weak. In the opposite and largely unexplored regime of
strongly correlated spinor condensates, three-body interactions can play an
important role through the Efimov effect, producing possible novel phases.
Here, we study the three-body spinor problem using the hyperspherical adiabatic
representation for spin-1, -2 and -3 condensates in the strongly-correlated
regime. We characterize the Efimov physics for such systems and the relevant
three-body mean-field parameters. We find that the Efimov effect can strongly
affect the spin dynamics and three-body mean-field contributions to the
possible quantum phases of the condensate through universal contributions to
scattering observables.
