Weyl Corrections Research Articles

Holographic superconductors with Weyl corrections

A quick review on the analytical aspects of holographic superconductors (HSCs) with Weyl corrections has been presented. Mainly, we focus on matching method and variational approaches. Different types of such HSC have been investigated — s-wave, p-wave and Stúckelberg ones. We also review the fundamental construction of a p-wave type, in which the non-Abelian gauge field is coupled to the Weyl tensor. The results are compared from numerics to analytical results.

Holographic p-wave superconductor models with Weyl corrections

We study the effect of the Weyl corrections on the holographic p-wave dual models in the backgrounds of AdS soliton and AdS black hole via a Maxwell complex vector field model by using the numerical and analytical methods. We find that, in the soliton background, the Weyl corrections do not influence the properties of the holographic p-wave insulator/superconductor phase transition, which is different from that of the Yang–Mills theory. However, in the black hole background, we observe that similarly to the Weyl correction effects in the Yang–Mills theory, the higher Weyl corrections make it easier for the p-wave metal/superconductor phase transition to be triggered, which shows that these two p-wave models with Weyl corrections share some similar features for the condensation of the vector operator.

Stellar stability in brane-worlds revisited

We consider here the general conditions for the stability of brane stars that obey a so called a minimal setup: the nonlocal anisotropic stress and energy flux are absent everywhere, and the only permitted Weyl correction is the interior solution of the nonlocal energy density. Along with a series of simple conditions, we show that the Germani–Maartens solution with a constant density sets up the upper bound for the compactness of that particular class of brane stars. The general demonstration is based upon the properties of the interior solutions of the stars, although we also show that the minimal setup implies a Schwarzschild exterior.

Rotating charged black hole with Weyl corrections

We present firstly a four-dimensional spherical symmetric black hole with small Weyl corrections and find that with increasing Weyl corrections the region of the event horizon existence for the black hole in the parameter space increases for the negative Weyl coupling parameter and decreases for the positive one. Moreover, we also obtain a rotating charged black hole with weak Weyl corrections by the method of complex coordinate transformation. Our results show that the sign of Weyl coupling parameter $\alpha$ yields the different spatial topology of the event horizons for the black hole with its parameters lied in some special regions in the parameter space. We also analyze the dependence of the ergosphere on the Weyl coupling parameter $\alpha$ and find that with the increase of the Weyl corrections the ergosphere in the equatorial plane becomes thick for a black hole with $\alpha>0$, but becomes thin in the case with $\alpha<0$, which means that the energy extraction become easier in the background of a black hole with the positive Weyl coupling parameter, but more difficult in the background of a black hole with the negative one.

Absorption cross section and Hawking radiation of the electromagnetic field with Weyl corrections

We have investigated the absorption cross section and the Hawking radiation of electromagnetic field with Weyl correction in the background of a four-dimensional Schwarzschild black hole spacetime. Our results show that the properties of the absorption cross section and the Hawking radiation depend not only on the Weyl correction parameter, but also on the parity of the electromagnetic field, which is quite different from those of the usual electromagnetic field without Weyl correction in the four-dimensional spacetime. With increase of Weyl correction parameter, the absorption probability, the absorption cross section, the power emission spectra and the luminosity of Hawking radiation decreases with Weyl correction parameter for the odd-parity electromagnetic field and increases with the even-parity electromagnetic field.

Holographic Superconductor Models with RF2 Corrections

We investigate the effect of the RF2 correction on the holographic superconductor model in the background of AdS black hole, where R is the Ricci scalar of spacetime and F2 = Fμν Fμν is the Maxwell field strength. We observe that, similar to the effect caused by the Weyl correction, the higher RF2 correction term can make it easier for the scalar operator to condense and result in the larger deviation from the expected relation in the gap frequency. However, we find that the condensation gap becomes larger as the RF2 correction term increases, which is in strong contrast to the influences of the Weyl correction and Gauss–Bonnet correction.

Dynamical evolution of the electromagnetic perturbation with Weyl corrections

We present firstly the master equation of an electromagnetic perturbation with Weyl correction in the four-dimensional black hole spacetime, which depends not only on the Weyl correction parameter, but also on the parity of the electromagnetic field. It is quite different from that of the usual electromagnetic perturbation without Weyl correction in the four-dimensional spacetime. And then we have investigated numerically the dynamical evolution of the electromagnetic perturbation with Weyl correction in the background of a four-dimensional Schwarzschild black hole spacetime. Our results show that the Weyl correction parameter $\alpha$ and the parities imprint in the wave dynamics of the electromagnetic perturbation. For the odd parity electromagnetic perturbation, we find it grows with exponential rate if the value of $\alpha$ is below the negative critical value $\alpha_c$. However, for the electromagnetic perturbation with even parity, we find that there does not exist such a critical threshold value and the electromagnetic field always decays in the allowed range of $\alpha$.

Analytic Study of Properties of Holographic Superconductors with Weyl Corrections

We analytically investigate the properties of holographic superconductors with Weyl corrections in AdS5-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. We find that the critical temperature of holographic superconductor with Weyl corrections increases as we amplify the Weyl coupling parameter γ, indicating the condensation will be harder when the parameter γ decreases. The critical exponent of the condensation also comes out to be 1/2 which is the universal value in the mean field theory.

Holographic insulator/superconductor phase transition with Weyl corrections

We analytically investigate the phase transition between the holographic insulator and superconductor with Weyl corrections by using the variational method for the Sturm–Liouville eigenvalue problem. We find that similar to the curvature corrections, in p-wave model, the higher Weyl couplings make the insulator/superconductor phase transition harder to occur. However, in s-wave case the Weyl corrections do not influence the critical chemical potential, which is in contrast to the effect caused by the curvature corrections. Moreover, we observe that the Weyl corrections will not affect the critical phenomena and the critical exponent of the system always takes the mean-field value in both models. Our analytic results are found to be in good agreement with the numerical findings.

CONDENSATION OF THE SCALAR FIELD WITH STUCKELBERG AND WEYL CORRECTIONS IN THE BACKGROUND OF A PLANAR AdS–SCHWARZSCHILD BLACK HOLE

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 m2. We show that in limit of the [Formula: see text] which is close to the numerical estimate [Formula: see text]. Further we show that the mass of the scalar field is bounded from below by the [Formula: see text] where [Formula: see text]. This lower bound is weaker and different from the previous lower bound m2 = -3 predicted by stability analysis. We show that in the Breitenlohner–Freedman bound, the critical temperature remains finite. Explicitly, we prove that here there exists a linear relation between 〈OΔ〉 and the chemical potential.

A NOTE ON HOLOGRAPHIC SUPERCONDUCTORS WITH WEYL CORRECTIONS

We study analytical properties of the holographic superconductors with Weyl corrections. We describe the phenomena in the probe limit neglecting backreaction of the spacetime. We observe that for the conformal dimension △+ = 3, the minimum value of the critical temperature [Formula: see text] at which condensation sets, can be obtained directly from the equations of motion as [Formula: see text], which is in very good agreement with the numerical value [Formula: see text] [Phys. Lett. B697, 153 (2011)]. This value of [Formula: see text] corresponds to the value of the Weyl's coupling γ = -0.06 in Table 1 of Phys. Lett. B697, 153 (2011). We calculate the [Formula: see text] for another Weyl's coupling γ = 0.02 and the conformal dimension △- = 1. Further, we show that the critical exponent is [Formula: see text]. We observe that there is a linear relation between the charge density ρ and the chemical potential difference μ-μ c qualitatively matches the numerical curves.

The [formula omitted] holographic superconductor with Weyl corrections

In this Letter we study 3+1 holographic superconductors with Weyl corrections. We find that the critical temperature of a superconductor with Weyl corrections increases as we amplify the Weyl coupling parameter γ, indicating the condensation will be harder when the parameter γ decreases. We also calculate the conductivity and the ratio of gap frequency over critical temperature ωg/Tc numerically for various coupling parameters. We find that the ratio ωg/Tc becomes larger when the Weyl coupling parameter γ decreases. We also notice that when γ<0 there is an extra spike that appears inside the gap.

Weyl corrections to holographic conductivity

For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk and thus obey universality relations at the classical level due to the uniqueness of the Maxwell action. We analyze corrections to these transport parameters due to higher-dimension operators in the bulk action, beyond the leading Maxwell term, of which the most significant involves a coupling to the bulk Weyl tensor. We show that the ensuing corrections to conductivity and the diffusion constant break the universal relation with the U(1) central charge observed at leading order, but are nonetheless subject to interesting bounds associated with causality in the boundary CFT.