  We obtain a holographical description of a superconductor by using the d=2
case of the AdS_{d+1}/CFT_d correspondence. The gravity system is a
(2+1)-dimensional AdS black hole coupled to a Maxwell field and charged scalar.
The dual (1+1)-dimensional superconductor will be strongly correlated. The
characteristic exponents for vector perturbations at the boundary degenerate,
which implies that d=2 is a critical dimension and the Green's function needs
to be regularized. In the normal phase, the current-current correlation
function and the conductivity can be analytically solved at zero chemical
potential. The dc conductivity can be analytically solved at finite chemical
potential. When we add a scalar hair to the black hole, a charged condensate
happens at low temperatures. We compare our results with higher-dimensional
cases.
