Abelian reductions of deformed ${\cal N}=4$ SYM

TL;DR

This paper demonstrates that a Fayet-Iliopoulos deformed ${ m N}=4$ SYM in 3+1 dimensions can be reduced to a relativistic Landau-Ginzburg model, with classical vortex solutions analyzed, extending previous work on ABJM models.

Contribution

It shows a new reduction of deformed ${ m N}=4$ SYM to a Landau-Ginzburg model, including the possibility of coupling to a real scalar, and studies classical vortex solutions.

Findings

Reduction to relativistic Landau-Ginzburg model with FI deformation

Existence of vortex solutions in the reduced model

Comparison with mass-deformed ${ m N}=4$ SYM results

Abstract

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.