  In this paper, we study a holographic dual of a confined fermi liquid state
by putting a charged fluid of fermions in the AdS soliton geometry. This can be
regarded as a confined analogue of electron stars. Depending on the parameters
such as the mass and charge of the bulk fermion field, we found three different
phase structures when we change the values of total charge density at zero
temperature. In one of the three cases, our confined solution (called soliton
star) is always stable and this solution approaches to the electron star away
from the tip. In both the second and third case, we find a
confinement/deconfinement phase transition. Moreover, in the third one, there
is a strong indication that the soliton star decays into an inhomogeneous
solution. We also analyze the probe fermion equations (in the WKB
approximation) in the background of this soliton star geometry to confirm the
presence of many fermi-surfaces in the system.

High Energy Physics - Theory;Strongly Correlated Electrons;General Relativity and Quantum Cosmology