arXiv:1008.3904v3 [hep-th] 16 Nov 2010 Preprint typeset in JHEP style - HYPER VERSIONPUPT-2347 One-dimensional holographic superconductor from AdS3/CFT2correspondence Jie Ren Department of Physics, Princeton University Princeton, NJ 08544, U.S.A. E-mail:jieren@princeton.edu Abstract:We obtain a holographical description of a superconductor by using thed= 2 case of the AdSd+1/CFTdcorrespondence. 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 per- turbations at the boundary degenerate, which implies thatd= 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 po- tential. 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. Keywords:AdS-CFT Correspondence, Black Holes, Field Theories in Lower Dimensions.
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