One-dimensional holographic superconductor from AdS3/CFT2 correspondence

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.