Analytical Holographic Superconductor with Backreaction Using AdS3/CFT2

TL;DR

This paper analytically investigates a two-dimensional holographic superconductor with backreaction effects using AdS3/CFT2, demonstrating how backreaction influences the critical temperature and condensation process.

Contribution

It introduces an analytical approach incorporating backreaction in holographic superconductors using Sturm-Liouville and perturbation methods, supporting previous numerical findings.

Findings

Critical temperature decreases with increased backreaction.

Backreaction makes condensation more difficult.

Analytical results align with prior numerical data.

Abstract

The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm-Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.