Phase transitions and linear response in strongly coupled systems: A holographic approach

Understanding strongly coupled systems is an important area of theoretical physics, and has wide ranging applications from quantum chromodynamics to condensed matter physics. This thesis uses holographic methods to understand two particular aspects of strongly coupled systems - linear response and phase transitions. Firstly, we consider a general class of electrical black holes in Einstein-Maxwell-scalar theory, that are holographically dual to conformal eld theories at nite charge density and explicitly break translational invariance. By considering the linearised perturbations of these background black holes, we show that the DC thermoelectric conductivity of these systems can be determined by solving a set of linearised Navier-Stokes equations on the event horizon of the dual black hole. We demonstrate how to apply this framework in practice with several examples. Next, we consider this framework in the hydrodynamic limit, for the simpler case of Einstein gravity. We show that the full stress-energy response, rather than just the thermal conductivity, can be determined in this limit, and compare the results with the uid/gravity correspondence. We then consider more general hydrodynamics, and demonstrate that periodically deformed eld theories exhibit thermal back ow when a DC thermal source is applied Finally, we study black hole solutions of type IIB supergravity that describe N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. We show that, by preserving additional scalar modes from the consistent truncation of IIB supergravity on the ve-sphere, these black holes have low temperature instabilities. We construct new thermodynamically preferred black hole solutions, and show that the phase transition between these black hole solution has unusual critical exponents that is not captured by the normal Landau-Ginzburg exponents. We consider various extensions to this, such as introducing a chemical potential, and construct a more complete phase diagram for the theory.Open Acces