  We analyze systems where an effective large-N expansion arises naturally in
gauge theories without a large number of colors: a sufficiently large charge
density alone can produce a perturbative string ('tHooft) expansion. One
example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times
S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is
completely stable, and we find that the existing string-theoretic solution of
this model yields two interesting results. First, it indicates that the shear
viscosity is not corrected by $\alpha'$ effects in this system. For flow
perpendicular to the F1 strings the viscosity to entropy ratio take the usual
value $1/4\pi$, but for flow parallel to the F1's it vanishes as $T^2$ at low
temperature. Secondly, it encodes singularities in correlation functions coming
from low-frequency modes at a finite value of the momentum along the $T^4$
directions. This may provide a strong coupling analogue of finite density
condensed matter systems for which fermionic constituents of larger operators
contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched
strings on the gravity side play the role of these composite operators. We
explore the analogue for our system of the Luttinger relation between charge
density and the volume bounded by these singular surfaces. This model provides
a clean example where the string-theoretic UV completion of the gravity dual to
a finite density field theory plays a significant and calculable role.
