On abelianizations of the ABJM model and applications to condensed matter

TL;DR

This paper explores abelian reductions of the ABJM model to better suit condensed matter applications, demonstrating how to obtain models with desired features by reduction and adding fundamental fields.

Contribution

It introduces an abelian reduction of the ABJM model that retains key features and shows how to incorporate fundamental fields for tailored condensed matter models.

Findings

A specific abelian reduction preserves essential properties.

Adding fundamental fields yields models with similar desired features.

Naive reduction fails to capture necessary condensed matter characteristics.

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.