Non-equilibrium aspects of the holographic duality - Silva, Giancarlo Thales Camilo da (2017)
This thesis is devoted to study far-from-equilibrium aspects of quantum systems at strong coupling using the holographic duality as a tool. The duality, originated from string theory and further generalized to broader scenarios, relates certain strongly coupled gauge theories to classical gravity theories in higher dimensions. Over the last years, it has proved itself useful as a calculational tool to map difficult questions of interest in the gauge theory into a dual (i.e., equivalent) problem in a higher-dimensional gravity language where the solution may become feasible. The interest in strongly coupled quantum field theories, in particular non-Abelian gauge theories, is motivated by a number of nuclear and condensed matter physics phenomena which are known to take place at a non-perturbative regime, such as the quark-gluon plasma phase of quantum chromodynamics or high-Tc superconducting materials. While dealing with strong coupling is typically a very hard task even at equilibrium, the situation becomes yet more dramatic when non-equilibrium setups are concerned since the main non-perturbative tool available nowadays lattice field theory suffers from serious problems when it comes to real-time dynamics. This is the reason why unconventional techniques such as the ones provided by holography are welcome. Of particular interest here are the problems of thermalization of strongly coupled plasmas as well as the quench dynamics of quantum systems, both of which admit a dual gravitational description involving time-dependent solutions to the corresponding classical equations of motion in the bulk of Anti de Sitter (AdS) spacetimes, such as collapsing solutions describing AdS black hole formation. Specifically, and always from a holographic point of view, in this thesis we deal with three classes of problems: the thermalization properties of a charged non-Abelian plasma after a sudden injection of energy (such as a heavy ion collision); the dynamics of a symmetry breaking quench process from a relativistic to a non-relativistic setup of the Lifshitz type with dynamical exponent z; and, finally, a new analytical approach to the non- equilibrium properties of conformal field theory plasmas placed in an expanding background. Apart from the specific problems, we also provide a self-contained but concise introduction to the holographic duality with a view towards newcomers with an elementary general relativity and quantum field theory background.