One-dimensional holographic superconductor from AdS_3/CFT_2 correspondence

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.

22 pages, 7 figures; v2: minor corrections; v3: published version

References in corpus (7)

• Building an AdS/CFT superconductor
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Holographic spectral functions and diffusion constants for fundamental matter
• The gravity dual to a quantum critical point with spontaneous symmetry breaking
• Hydrodynamics from the D1-brane
• Spinning Dragging Strings

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• Symmetric solitonic excitations of the (1+1)-dimensional Abelian-Higgs "classical vacuum"
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