Holographic descriptions of collective modes in strongly correlated media

Abstract: Solving the puzzle of high temperature superconductivity may be one of the most desired scientific breakthroughs of our time, as access to room temperature superconductivity could revolutionize society as we know it. In this thesis, we strive to increase the theoretical understanding of such matter, by studying the phase above, in temperature, the superconducting phase - the "strange metal". The strange metal phase is a phase characterized by the absence of a quasi-particle description. The electrons in this phase are strongly coupled, which means that conventional methods, such as perturbation theory in quantum field theory and Monte Carlo methods fall short of being able to describe their dynamics. Perhaps surprisingly, string theory provides a different method, capable of describing precisely such systems - the holographic duality. Whereas there has been significant effort devoted to the applications of the duality since its inception in 1997, and even more so in the last decade after it was observed that it worked remarkably well for condensed matter theory, it wasn't until our project that the dynamical polarization of such strongly coupled systems where properly treated. In this thesis, we introduce the minimal constraints required for a sensible description of a polarizing medium, and convert those to boundary conditions to the equations of motion provided by the holographic dual. These boundary conditions deviate from previous holographic studies, and we contrast the quasinormal modes previously studied with the emergent collective modes we find for some different models. We find novel results, as well as confirm the predictions of less general models in their respective regions of validity and pave the way for more complex future models.