  Following the work in \cite{Mohammed:2012gi}, where the massive ABJM model in
2+1 dimensions was shown to have an abelian reduction to the relativistic
Landau-Ginzburg, and motivated by the implications for condensed matter through
AdS/CFT, we show that a FI deformation of ${\cal N}=4$ SYM in 3+1 dimensions
with a mass term can also be reduced to a relativistic Landau-Ginzburg model,
with the possibility of coupling it to a real scalar, whereas the simply mass
deformed ${\cal N}=4$ SYM reduces only to a massive $\phi^4$ model (scalar QED)
coupled to a real scalar. We study the classical solutions of the model, in
particular vortex solutions.
