  In this paper we study a simple gravity model dual to a (2+1)-dimensional
system with a boundary at finite charge density and temperature. In our naive
AdS/BCFT extension of a well known AdS/CFT system a non-zero charge density
must be supported by a magnetic field. As a result, the Hall conductivity is a
constant inversely proportional to the coefficients of pertinent topological
terms. Since the direct conductivity vanishes, such behaviors resemble that of
a quantum Hall system with Fermi energy in the gap between the Landau levels.
We further analyze the properties stemming from our holographic approach to a
quantum Hall system. We find that at low temperatures the thermal and electric
conductivities are related through the Wiedemann-Franz law, so that every
charge conductance mode carries precisely one quantum of the heat conductance.
From the computation of the edge currents we learn that the naive holographic
model is dual to a gapless system if tensionless RS branes are used in the
AdS/BCFT construction. To reconcile this result with the expected quantum Hall
behavior we conclude that gravity solutions with tensionless RS branes must be
unstable, calling for a search of more general solutions. We briefly discuss
the expected features of more realistic holographic setups.
