  In this paper we initiate the study of holographic quantum liquids in 1+1
dimensions. Since the Landau Fermi liquid theory breaks down in 1+1 dimensions,
it is of interest to see what holographic methods have to say about similar
models. For theories with a gapless branch, the Luttinger conjecture states
that there is an effective description of the physics in terms of a Luttinger
liquid which is specified by two parameters. The theory we consider is the
defect CFT arising due to a probe D3 brane in the AdS Schwarzschild planar
black hole background. We turn on a fundamental string density on the
worldvolume. Unlike higher dimensional defects, a persistent dissipationless
zero sound mode is found. The thermodynamic aspects of these models are
considered carefully and certain subtleties with boundary terms are explained
which are unique to 1+1 dimensions. Spectral functions of bosonic and fermionic
fluctuations are also considered and quasinormal modes are analysed. A
prescription is given to compute spectral functions when there is mixing due to
the worldvolume gauge field. We comment on the Luttinger conjecture in the
light of our findings.
