Non-Relativistic Holography from Hořava Gravity Stefan Janiszewski Chair of the Supervisory Committee:Professor Andreas Karch Department of PhysicsHolography is a powerful theoretical duality that relates quantum gravitational theories to non-gravitational theories in one less dimension. The most explored example of this tool is the correspondence between general relativity on five dimensional Anti-deSitter space and a four dimensional supersymmetric Yang-Mills theory. This case is extremely useful as the strong coupling regime of the Yang-Mills theory is solved by weakly coupled gravity.Another interesting class of strongly coupled field theories are those of a nonrelativistic nature that arise in condensed matter systems. Herein, motivated by the generic symmetry structure of these theories, a non-relativistic version of holography is proposed using an alternate theory of gravity, Hořava gravity. Justifications of this proposal are thoroughly discussed. Various checks of the duality, such as correlation functions and black hole thermodynamics are presented. This new holographic correspondence provides a crucial tool to tackle strongly coupled problems in condensed matter systems. On the other hand, Hořava gravity, thought to be a UV complete theory of quantum gravity, will allow holography to move away from the strong coupling, large number of colors limit that has restricted traditional AdS/CFT.

Detailed knowledge about equilibration processes is of interest for various fields of physics, including heavy ion collision experiments and quantum quenched condensed matter systems. We study the approach to equilibrium at late times within two types of strongly coupled thermal systems in 3 + 1 dimensions: systems in the presence of (i) a non-zero charge density, or (ii) a magnetic field at vanishing charge density. Utilizing the gauge/gravity correspondence, we map the aforementioned problem to the computation of quasinormal frequencies around two particular classes of black branes within the Einstein-Maxwell theory. We compute (i) the tensor and vector quasinormal modes of Reissner-Nordström black branes and (ii) the scalar, as well as tensor quasinormal modes of magnetic black branes. Some of these quasinormal modes correspond to the late-time relaxation of the above systems after starting with initial pressure anisotropy. We provide benchmarks which need to be matched at late-times by all holographic thermalization codes with the appropriate symmetries.

We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.

Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.