Black Hole Holographic Superconducting Phase Transition

Holographic superconductors are strongly coupled field theories which undergo a superconducting phase transition below a critical temperature, and which have a gravity dual in the sense of the AdS/CFT correspondence.The reason for considering these systems is that they admit a large N limit in which many aspects of the physics can be studied directly, despite the theory being inherently strongly coupled.From the (d dimensional) field theory point of view, superconductivity is charac-terised by the condensation of a, generically composite, charged operator O for low temperatures T<Tc. In the dual (d+1dimensional) gravitational description of the system, the transition to superconductivity is observed as a classical instability of a black hole in anti-de Sitter (AdS) space against perturbations by a charged scalar field ψ. The instability appears when the black hole has Hawking temperature T=Tc. For lower temperatures the gravitational dual is a black hole with a nonvanishing profile for the scalar field ψ The AdS/CFT correspondence relates the highly quantum dynamics of the ’boundary’ operator O to simple classical dynamics of the ’bulk’ scalar field ψIn the second section, we introduce the concepts of holographic superconductors by building a superconductor in the asymptotic AdS4background and also show some numerical results on the condensation in low temperature phase. In the third sec-tion, we both talk about the model describing a charged, complex scalar field into the3-dimensional Einstein-Maxwell action with negative cosmological constant and the model describing the Born-Infeld field and a charged complex scalar field in the five-dimensional Einstein-Gauss-Bonnet spacetime with negative cosmological con-stant. We analytically solve Einstein equations and the equation of motions of gauge field in high temperature phase and obtain an anti-de Sitter black hole and Born-Infeld electromagnetic field. Further, we consider the classical instability of black holes in anti-de Sitter space against perturbations by a charged scalar field. On the basis of the response function, we deeply study the critical behaviors of the system near the critical point. So far, we have concentrated on the planar spacetime, for a holographic super-conductor with spherical or hyperbolic topology, one can’t get the solution analytically or numerically. Thus, we study a holographic superconductor with spherical topology in the high temperature to win some information on such a model.Besides, in the forth section, we also study the charged scalar condensation in the low temperature for the3D and5D holographic superconductors. We consider the backreaction imposed by extra field on the operator O in3D holographic supercon-ductor, reaching the conclusion that the gaps of the operator of mass dimension one aren’t consistent with critical temperature, which indicates that the operator of mass dimension one is less physical. In the low temperature phase of the5D Gauss-Bonnet-Born-Infeld-AdS holographic model, we study the influence of backreaction, Gauss-Bonnet factor, and Born-Infeld factor on the condensation. Furthermore, we also study the mechanics of two kind of classical instability of the AdS black hole against the perturbation of a charged scalar. We also investigate the influence of backreaction, Gauss-Bonnet factor, and Born-Infeld factor on the conductivity.