One-dimensional holographic superconductor from AdS_3/CFT_2 correspondence

TL;DR

This paper models a (1+1)-dimensional superconductor using holography via a (2+1)-dimensional AdS black hole, revealing critical behavior and analytical solutions for conductivity and phase transition.

Contribution

It provides the first holographic description of a 1+1D superconductor using AdS3/CFT2, highlighting critical dimension effects and analytical results for conductivity.

Findings

Analytical solutions for current-current correlation and conductivity at zero chemical potential.

Charged condensate formation at low temperatures with scalar hair added.

Identification of d=2 as a critical dimension with degenerate boundary exponents.

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.