Abelian reductions of deformed N=4SYM

Following the work in [1], where the massive ABJM model in 2 +1dimensions 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 N=4SYM in 3 +1dimensions 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 N=4SYM reduces only to a massive φ⁴ model (scalar QED) coupled to a real scalar. We study the classical solutions of the model, in particular vortex solutions. (author)