  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.
