Non-Relativistic Holography from Horava Gravity

Thesis (Ph.D.)--University of Washington, 2014Holography 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-de Sitter 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 non-relativistic 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, Horava 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, Horava 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