Analytic study of properties of holographic p-wave superconductors

TL;DR

This paper analytically investigates the properties of p-wave holographic superconductors in an AdS-Schwarzschild background, deriving key relations and confirming results with existing numerical data.

Contribution

It introduces two analytical approaches to study p-wave holographic superconductors and confirms the universal critical exponent of 1/2.

Findings

Relation between critical temperature and charge density derived

Expectation value of condensation operator's temperature dependence found

Critical exponent of 1/2 confirmed

Abstract

In this paper, we analytically investigate the properties of p-wave holographic superconductors in $AdS_{4}$-Schwarzschild background by two approaches, one based on the Sturm-Liouville eigenvalue problem and the other based on the matching of the solutions to the field equations near the horizon and near the asymptotic $AdS$ region. The relation between the critical temperature and the charge density has been obtained and the dependence of the expectation value of the condensation operator on the temperature has been found. Our results are in very good agreement with the existing numerical results. The critical exponent of the condensation also comes out to be 1/2 which is the universal value in the mean field theory.