Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation

TL;DR

This paper embeds a 3D condensed matter model into a higher-dimensional string theory framework by truncating a complex gauge theory to an abelian effective theory, linking condensed matter physics and gravity via dimensional reduction.

Contribution

It introduces a consistent abelian truncation of the ABJM model that interpolates between different effective theories, providing a bridge between condensed matter models and string theory.

Findings

Derived an abelian effective field theory from the ABJM model.

Connected the abelianization process to dimensional reduction.

Proposed a condensed matter model capturing key features of the abelianization.

Abstract

We present an embedding of the 3-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an $\mathcal{N}=6$, $U(N)\times U(N)$ Chern-Simons-matter theory (the ABJM model) by consistently truncating the latter to an abelian effective field theory encoding the collective dynamics of ${\cal O}(N)$ of the ${\cal O}(N^2)$ modes. In fact, depending on the VEV on one of the ABJM scalars, a mass deformation parameter $\mu$ and the Chern-Simons level number $k$, our abelianization prescription allows us to interpolate between the abelian Higgs model with its usual multi-vortex solutions and a $\phi^4$ theory. We sketch a simple condensed matter model that reproduces all the salient features of the abelianization. In this context, the abelianization can be interpreted as giving a dimensional reduction from four dimensions.