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arXiv · 1008.3904

One-dimensional holographic superconductor from AdS_3/CFT_2 correspondence

Jie Ren
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Abstract

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.

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Jie Ren. 2010-08-23. One-dimensional holographic superconductor from AdS_3/CFT_2 correspondence. https://doi.org/10.1007/jhep11(2010)055

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