(In)stability and excitation of modes in (asymptotically) Anti-de Sitter space-times with view to the AdS/CFT correspondence

Abstract

The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence is one of the most important results of String Theory and is the best tested example of the more general gauge/gravity duality. It states that a String theory in Anti-de Sitter space-time (AdS) is dual to a Conformal Quantum Field Theory (CFT) on the boundary of AdS. In particular, the duality connects strongly coupled Quantum Field Theories in d space-time dimensions to weakly coupled gravity theories in (d+1) dimensions and as such is also often denoted to be holographic.In recent years it has been suggested that this fact can be used to gain easier excess to strongly coupled Quantum Field Theories. Examples are real-time, high density processes in Quantum Chromodynamics as well as high temperature superconductivity which is presumably driven by strong interaction processes. In both cases experimental data exists which can be used to test the correspondence. In this context, it is, of course, of great importance to understand the stability of space-times that are asymptotically AdS and even the stability of AdS itself. For static and stationary cases, the instability of black hole and soliton solutions to the formation of non-trivial fields in their asymptotically AdS space-times can be used to describe non-vanishing expectation values of the operators of the dual field theory. Moreover, the description of dynamical processes in AdS is of huge interest with view to the dual theory, but has also significancewhen studying fundamental properties such as the non-linear (in)stability of AdS itself. Recent results suggest that the excitation of modes inherent to the systems under study play a fundamental role. This project aims at shedding further light on both topics by (a) studying static and stationary situations in asymptotically AdS that allowto describe more structure in the dual field theory and (b) making an in-depth analysisof dynamical situations in AdS by using simple systems in lower dimensions and clarifying the role of excited modes in these cases. (AU)