Holography, Fractionalization and Magnetic Fields

TL;DR

This paper constructs zero-temperature electron star solutions in Einstein-Maxwell-dilaton theory with magnetic fields, revealing how fractionalized degrees of freedom behave in strongly coupled (2+1)-dimensional systems under magnetic influence.

Contribution

It introduces novel electron star solutions in a magnetic background, elucidating the interplay between fractionalization and magnetic fields in holographic models.

Findings

Electron star solutions cloak magnetic sources with horizons.

Charge and energy densities reduce to free fermion results in star limits.

Three types of solutions with different horizon and star configurations are constructed.

Abstract

Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon.