The thesis is devoted to applications of the anti de Sitter/Conformal field theory correspondence (AdS/CFT, also called holography) to various problems in different areas of theoretical physics. We... Show moreThe thesis is devoted to applications of the anti de Sitter/Conformal field theory correspondence (AdS/CFT, also called holography) to various problems in different areas of theoretical physics. We make use of AdS/CFT to get insights into the physics of superconductors, quark-gluon plasma, and to study properties of quantum field theories on non-causal backgrounds. In the first part of the thesis we construct a holographic model of a Bardeen-Cooper-Schrieffer-like superconductor and demonstrate that the Cooper instability of Fermi-liquids can be naturally described in holographic terms. We show that both the superconducting phase and the BEC/BCS crossover appear naturally. In the second part we address the problem of quark-gluon plasma formation in heavy ion collisions. We study the effect of finite chemical potential on this process and calculate physical properties of the resulting deconfined state. The third part is dedicated to study of evolution of a quantum system with violated causality. Using AdS/CFT we can map the complicated and poorly defined non-causal quantum dynamics onto a classical spacetime with closed timelike curves. Doing that we have derived the Green's function of the QFT and demonstrated that evolution of a quantum system can be consistent and non-pathological even at broken causality. Show less
