  We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged
Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such
reduction gives a Toda system, for which we find a new type of nonabelian
vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to
embed all the usual (multi-)vortex solutions of the latter into the ABJM model.
By turning off the mass deformation at the level of the reduced model, we can
also continuously deform to the massive $\phi^4$ theory in the massless ABJM
case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT
correspondence as a consistent truncation of ABJM. In this context, the mass
deformation parameter $\mu$ and a field VEV $<\phi>$ act as $g$ and $g_c$
respectively, leading to a well-motivated AdS/CMT construction from string
theory. To further this particular point, we propose a simple model for the
condensed matter field theory that leads to an approximate description for the
ABJM abelianization. Finally, we also find some BPS solutions to the
mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending
on a spherical M5-brane.
