The theoretical description of fermionic system with strong interaction is a very challenging open problem in physics. The most notable (but far from the only) experimental realization of this... Show moreThe theoretical description of fermionic system with strong interaction is a very challenging open problem in physics. The most notable (but far from the only) experimental realization of this type of systems are the cuprate superconductors which have zero electric resistivity. Even if onehas a good microscopic model for the description of these materials it is very hard to translate it to macroscopic observables which in principle can be experimentally checked. The problem is that in case of a relevant interaction one can not Taylor expand in the coupling constant in the low-energy regime in which we are most interested. On the other hand, because of the fermion sign problem Monte Carlo numerical techniques (which are succesful with bosonic models) do not work for fermions at finite density. This thesis is devoted to the applications of several methods to the research area described above. The common theme of these techniques is that they are (partly) motivated from high-energy physics: the research area which deals with particle physics, string theory etc. Show less
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
We employ the novel method of AdS/CFT correspondence to study strongly correlated fermions, their ground states and the phase transitions between them. AdS/CFT maps the quantum many-body problem to... Show moreWe employ the novel method of AdS/CFT correspondence to study strongly correlated fermions, their ground states and the phase transitions between them. AdS/CFT maps the quantum many-body problem to a classical gravity problem, making it more tractable. We find a holographic description of Fermi liquids and then proceed to find novel non-Fermi liquid ground states. In the future one can expect AdS/CFT to contribute toward our understanding of real world materials. Show less
As one of the most important developments in string theory, the AdS/CFT correspondence(or in general gauge/gravity correspondence) encodes a way of using string theory to perform non-perturbative... Show moreAs one of the most important developments in string theory, the AdS/CFT correspondence(or in general gauge/gravity correspondence) encodes a way of using string theory to perform non-perturbative calculation in gauge theory which is still a complicated problem. It was firstly formulated as the correspondence between weakly coupled gravity theory with AdS (Anti de Sitter) space-time background and strongly coupled gauge theory with conformal symmetry in one lower dimension. One application of AdS/CFT is to compute some of observables of sQGP such as photon and dilepton production rates, mean-free path time of the plasma constituents, and anisotropic drag force effect to the elliptic flow. Show less
