On abelianizations of the ABJM model and applications to condensed matter

Abstract

In applications of AdS/CFT to condensed matter systems in 2+1 dimensions, the ABJM model is often used, however the condensed matter models are usually abelian and contain charged fields. We show that a naive reduction of the ABJM model to N=1 does not have the desired features, but we can find an abelian reduction that has most features, and we can also add fundamental fields to the ABJM model to obtain other models with similar properties.