UC Santa Barbara

This dissertation investigates thermal holographic quantum field theories dual to gravitational systems with black holes. This study has relevance for experimental physics in a lab or near an astrophysical black hole as well as for the structure of higher dimensional quantum field theories. The dissertation begins with an introduction to AdS/CFT, entanglement entropy, and numerical methods.

The next two chapters explore constraints on holographic quantum field theories with a semi-classical dual. In chapter two, a scalar field is used to construct an ``extended wormhole'' that connects two identical asymptotic regions and is globally static. Mutual information of identical regions in the two boundary CFTs show that the expanded throat corresponds to rapid thermalization in the field theory. In the third chapter, a finite temperature phase transition in the gravitational path integral is used to constrain the spectrum of charged, spinning operators in the dual thermal CFT.

The fourth and fifth chapters are concerned with the study of thermal quantum field theories around black holes. In chapter four, the holographic dual of a zero-temperature quantum field theory on a finite temperature Reissner-Nordstr{\"o}m black hole background is constructed. The entanglement entropy of annular regions in the field theory explains a phenomenon called ``jamming,'' in which heat flow is impeded due to strong interactions. In chapter five, the holographic dual to a quantum field theory on the interior of a doubly-spinning Myers-Perry black hole is constructed. The null energy along the Cauchy horizon diverges negatively, indicating singular behavior and providing evidence for strong cosmic censorship.

The sixth chapter constructs the holographic dual to a strongly interacting metal with charged bosonic excitations. Such a field theory is a candidate system to describe the pseudogap phase of the high temperature superconductors. Experiments on these systems exhibit a metal-insulator transition at zero temperature and power-law conductivities at low temperature. On the gravity side, a domain wall potential for a scalar field interpolates between UV and IR conformally invariant spacetimes with different length scales. The dimension of the scalar controls the temperature and frequency dependence of the low temperature conductivity.