  We study properties of strongly coupled CFT's with non-zero background
electric charge in 1+1 dimensions by studying the dual gravity theory - which
is a charged BTZ black hole. Correlators of operators dual to scalars, gauge
fields and fermions are studied at both T=0 and $T\neq 0$. In the $T=0$ case we
are also able to compare with analytical results based on $ AdS_2$ and find
reasonable agreement. In particular the correlation between log periodicity and
the presence of finite spectral density of gapless modes is seen. The real part
of the conductivity (given by the current-current correlator) also vanishes as
$\omega \rightarrow 0$ as expected. The fermion Green's function shows
quasiparticle peaks with approximately linear dispersion but the detailed
structure is neither Fermi liquid nor Luttinger liquid and bears some
similarity to a "Fermi-Luttinger" liquid. This is expected since there is a
background charge and the theory is not Lorentz or scale invariant. A boundary
action that produces the observed non-Luttinger-liquid like behavior
($k$-independent non-analyticity at $\omega=0$) in the Greens function is
discussed.
