Real-Time Finite-Temperature Holography and its Applications

This dissertation begins with a brief review of basic concepts of holography (AdS/CFT correspondence, Chapter 1). A complete prescription for computing real-time correlators in strongly-coupled conformal field theories at finite-temperature using holography is proposed and checked, and all scalar real-time 3-point correlators of the relativistic conformal field theory are computed at the tree level of dual gravity theory (Chapter 2). The causal 3-point correlators are found to have a simple structure which can be easily generalized to higher n-point correlators and higher spin operators.Then the same prescription is applied to non-relativistic holography (Chapter 3). All scalar real-time 2-point correlators and time-ordered and causal 3-point correlators of finite-temperature Schr¨odinger field theory are computed there. In the last two chapters, the prescription for relativistic real-time finite-temperature holography and in particular the causal 3-point correlators derived earlier, are used to study various properties of a strongly-coupled plasma, specifically that of N = 4 supersymmetric Yang-Mills field theory. By computing causal energy-stress tensor 3-point correlators analytically in the hydrodynamic regime and matching them with the holographic
result, and through the use of newly developed second order Kubo formulae, all five second order transport coefficients of the relativistic conformal hydrodynamics are systematically and consistently computed (Chapter 4). Jet quenching in a stronglycoupled plasma at finite-temperature and finite-chemical potential is also studied by an analytic computation of causal R-current 3-point correlators in large momentum regime. A more detailed and comprehensive picture than previously known emerges (Chapter 5). The dependence of typical jet stopping distance on its initial energy has an exponent 1/4, rather than the 1/3 which was widely known, and the jet quenching is enhanced by introducing a chemical potential to the system.

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