# One-dimensional backreacting holographic p-wave superconductors

## TL;DR

This paper investigates one-dimensional holographic p-wave superconductors with backreaction, using analytical and numerical methods to analyze critical temperature, phase transition order, and the effects of backreaction and mass parameters.

## Contribution

It provides a combined analytical and numerical study of backreacting 1D holographic p-wave superconductors, highlighting how backreaction and mass influence critical temperature and phase transition.

## Key findings

- Critical temperature increases with backreaction and mass.
- Phase transition is second order with a critical exponent of 1/2.
- Analytical and numerical results are in good agreement.

## Abstract

We analytically as well as numerically study the properties of one-dimensional holographic p- wave superconductors in the presence of backreaction. We employ the Sturm-Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the AdS3/CFT2 correspondence and determine the relation between the critical temperature Tc and the chemical potential \mu for different values of mass m of charged spin-1 field and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find out that increasing the backreaction as well as the mass parameter cause the greater values for Tc/ \mu. Therefore, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent \beta is 1/2 which is the same as in the mean field theory. Moreover, both methods confirm the exhibition of a second order phase transition.