Condensation of the scalar field with Stuckelberg and Weyl Corrections in the background of a planar AdS-Schwarzschild black hole

TL;DR

This paper analytically investigates Stuckelberg holographic superconductors with Weyl corrections in an AdS-Schwarzschild background, deriving critical temperature bounds and relations between order parameters and chemical potential.

Contribution

It provides analytical expressions for critical temperature and bounds on scalar field mass, extending understanding of holographic superconductors with Weyl corrections.

Findings

Critical temperature approximates numerical results for specific scalar mass.

Scalar field mass has a lower bound different from previous stability bounds.

Critical temperature remains finite within the Breitenlohner-Freedman bound.

Abstract

We study analytical properties of the Stuckelberg holographic superconductors with Weyl corrections. We obtain the minimum critical temperature as a function of the mass of the scalar field $m^2$. We show that in limit of the $m^2=-3$,$T^{Min}_c\approx0.158047\sqrt[3]{\rho}$ which is close to the numerical estimate $T_c^{Numerical}\approx 0.170\sqrt[3]{\rho}$. Further we show that the mass of the scalar field in bounded from below by the $ m^2>m_c^2$ where $m_c^2=-5.40417$. This lower bound is weaker and different from the previous lower bound $m^2=-3$ predicted by stability analysis. We show that in the Breitenlohner-Freedman bound, the critical temperature remains finite. Explicitly, we prove that here there is exist a linear relation between $<O_{\Delta}>$ and the chemical potential.