Holographic superconductors with Weyl Corrections via gauge/gravity duality

TL;DR

This paper analytically investigates p-wave holographic superconductors with Weyl corrections, deriving relations between critical temperature, charge density, and condensate behavior, confirming previous numerical and variational findings.

Contribution

It provides an analytical computation of key parameters of Weyl-corrected p-wave holographic superconductors, establishing explicit formulas and confirming numerical results.

Findings

Critical temperature scales as T_c ∝ ρ^{1/3}

Condensate expectation value scales as T_c^{3/2} T^{Δ-1/2} sqrt(1-(T/T_c)^3)

Critical exponent is 1/2, independent of Weyl coupling γ

Abstract

In this paper, we analytically compute the basic parameters of the p-wave holographic superconductors with Weyl geometrical corrections using the matching method. The explicit correspondence between the critical temperature $T_c$ and the dual charge density $\rho$ has been calculated as $T_c\propto\rho^{{1}{3}}$ and the dependence of the vacuum expectation value for the dual condensate operator $\cal{O}$ on the temperature has been found analytically in the form $<{\cal O}_{+}>\propto T_c^{{3}{2}}T^{\Delta-{1}{2}}\sqrt{1-({T}{T_c})^3}$. The critical exponent ${1}{2}$ is an universal quantity according to predictions of the mean field theory and independent from the Weyl coupling $\gamma$. Our analytical results confirm the numerical results and also agree on computations using by the variational method.