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Ngo Thanh, Hai (2011): Gauge/gravity duality: From quantum phase transitions towards out-of-equilibrium physics. Dissertation, LMU München: Faculty of Physics
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Abstract

In this dissertation we use gauge/gravity duality to investigate various phenomena of strongly coupled field theories. Of special interest are quantum phase transitions, quantum critical points, transport phenomena of charges and the thermalization process of strongly coupled medium. The systems studied in this thesis might be used as models for describing condensed matter physics in a superfluid phase near the quantum critical point and the physics of quark-gluon plasma (QGP), a deconfinement phase of QCD, which has been recently created at the Relativistic Heavy Ion Collider (RHIC). Moreover, we follow the line of considering different gravity setups whose dual field descriptions show interesting phenomena of systems in thermal equilibrium, slightly out-of-equilibrium and far-from-equilibrium. We first focus on systems in equilibrium and construct holographic superfluids at finite baryon and isospin charge densities. For that we use two different approaches, the bottom-up with an U(2) Einstein-Yang-Mills theory with back-reaction and the top-down approach with a D3=D7 brane setup with two coincident D7-brane probes. In both cases we observe phase transitions from a normal to a superfluid phase at finite and also at zero temperature. In our setup, the gravity duals of superfluids are Anti-de Sitter black holes which develop vector-hair. Studying the order of phase transitions at zero temperature, in the D3=D7 brane setup we always find a second order phase transition, while in the Einstein-Yang-Mills theory, depending on the strength of the back-reaction, we obtain a continuous or first order transition. We then move to systems which are slightly out-of-equilibrium. Using the D3/D7 brane setup with Nc coincident D3-branes and Nf coincident D7-brane probes, we compute transport coefficients associated with massive N = 2 supersymmetric hypermultiplet fields propagating through an N = 4 SU(Nc) super Yang-Mills plasma inthe limit of Nf << Nc. Introducing a baryon number density and arbitrary constant electric and magnetic fields, we compute all components of the conductivity tensor associated with transport of baryon number charge. Determining the contribution that the flavor degrees of freedom make to the stress-energy tensor, we are able to identify the rates of energy and momentum loss of the flavor field to the plasma. Going towards systems far-from-equilibrium, we investigate a time-dependent geometry consisting of a mirror moving in the bulk of the Anti-de Sitter space. This geometry can be seen as a toy model which is relevant to the formulation of holographic thermalization in strongly coupled field theory. For this configuration, we establish a procedure for calculating time-dependent two-point functions of scalar fluctuations, based on a WKB approximation. We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with the geometric optics.