Thermodynamics, Hydrodynamics and Critical Phenomena in Strongly Coupled Gauge Theories

The gauge theory / string theory correspondence has led to great progress in the study of strongly-coupled gauge theories. In this work, we start with a detailed treatment of some simple examples of this correspondence in order to establish some of the concepts and techniques are used on a more complicated system. We then consider a (3+1)-dimensional theory of gravity with a translationally invariant horizon, that is assumed to be dual to a (2+1)-dimensional non-conformal gauge theory at finite temperature. We study the thermodynamics of this model and find that there exists an exotic type of second-order phase transition wherein the symmetry-broken phase occurs above the critical temperature. We also study the hydrodynamics of this model and find that the speed of sound in the various phases of the model suggests that the symmetry broken phases are thermodynamically stable, yet their higher free energy with respect to the symmetric phase suggests that they are not thermodynamically preferred. We calculate the bulk-to-shear viscosity ratio and find that, in the symmetry-broken phase, it diverges at the phase transition. Finally, we study the critical behaviour of this model close to the phase transition and compute the static and dynamic critical exponents, which turn out to be of mean-field type. We conclude that, although the symmetry-broken phases are thermodynamically stable, they are perturbatively unstable. Thus, this model is a counter-example to the Correlated Stability Conjecture, which relates thermodynamic and classical (in)stabilities of black branes with translationally invariant horizons