Holographic Superconductors And Holographic Entanglement Entropy In Nonlinear Electrodynamics

As a concrete realization of the holographic principle, the AdS/CFT dual-ity relates strongly interacting gauge theories with large numbers of colors to weakly coupled gravitational theories with negative cosmological constant. It in-dicates that a gravity theoryin a d+1-dimensional anti-de Sitter spacetime can be completely described by a conformal field theory on the d-dimensional boundary. By using this powerful correspondence, one can investigate various phenomena of strongly coupled field theories. Especially, this theory has been fruitfully applied to the study of the holographic superconductor and holographic entanglement en-tropy. In this paper, we focus on the study of the holographic superconductor in Gauss-Bonnet gravity with Born-Infeld electrodynamics and the Born-Infeld holographic entanglement entropy in phase transition.In chapter 1, we brief introduce the holographic principle and the AdS/CFT duality’s dedinition, the holographic superconductors model’s establishment, sta-tus and significance, and the holographic entanglement entropy’s investigation and status.In chapter 2, we numerically and analytically study the holographic super-conductors for Born-Infeld electrodynamics in Gauss-Bonnet gravity with back-reactions. We note that the analytic method is still powerful for this complex system and the results obtained by the analytical and numerical computations are consistent. We find that the critical temperature decreases with the increase of the backreactions, Gauss-Bonnet, and Born-Infeld parameters, which means that increase of the strength of these effects will make the scalar hair harder to form. Furthermore, the Gauss-Bonnet factor modifies the critical temperature more sig-nificantly than the backreaction factor. The effect of the Born-Infeld factor on the critical temperature is weaker than the backreaction factor. We also show that the critical exponent is not affected by the backreactions, Gauss-Bonnet gravity, and Born-Infeld electrodynamics.In chapter 3, we study the the holographic entanglement entropy in nonlinear electrodynamics. In insulator/superconductor phase transition, considering the backreaction of the material field on the gravity, we investigate the holographic entanglement entropy in five-dimensional AdS soliton spacetime. We note that the holographic entanglement entropy is a good probe to study the properties of the phase transition. At the critical point the entanglement entropy is continuous but its slope has a discontinuous change. Consequently, this phase transition can be regarded as the second order one, and the Born-Infeld factor b has no effect on the critical chemical potential μc. We find that both in the half space and the belt one, the non-monotonic behavior of the entanglement entropy versus the chemical potential is a general property, and the entanglement entropy increases with the increase of the Born-Infeld factor in the superconductor phase. Particularly, there exist confinemcnt/deconfinement phase transition in the strip geometry and the critical width lc is dependent on the Born-Infeld parameter.In metal/superconductor phase transition, we studied the holographic entan-glement entropy for Born-Infeld electrodynamics. We found the holographic en-tanglement entropy is a good probe to study the properties of the phase transition. For the operator< O_>, we find that the entanglement entropy decreases (or increases) with the increase of the Born-Infeld parameter b in the metal (or super-conducting) phase. For the operator< 0+>, we observe that, with the increase of the Born-Infeld parameter, the entanglement entropy in the metal phase decreases monotonously but the entropy in the superconducting phase first increases and forms a peak at some threshold bT, then decreases continuously. Furthermore, the value of bT becomes smaller as the width of the subsystem A decreases.In chapter 4, we give a summary and a outlook of holographic superconductors and holographic entanglement entropy.