Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Oliver DeWolfe

Second Advisor

Senarath de Alwis

Third Advisor

Thomas DeGrand

Fourth Advisor

Andrew Hamilton

Fifth Advisor

Paul Romatschke

Abstract

We apply holographic duality to the study of strongly interacting quantum matter. The correspondence between the four-dimensional N=8 gauged supergravity and the three-dimensional superconformal ABJM quantum field theory allows us to study the latter theory by performing computations in the former. Asymptotically anti-de Sitter spacetimes satisfying the classical supergravity equations of motion are interpreted as states of strongly interacting ABJM theory. If such a spacetime sources an electric field, the dual state is at non-zero charge density.

Interesting observables of such states include spectral functions of fermionic operators - we compute these by solving Dirac equations in a variety of spacetimes. In a family of extremal charged black holes, we find Fermi surface singularities with non-Fermi liquid characteristics. In a special "three-charge" black hole, an interval appears in the spectral functions within which the fermionic excitations are perfectly stable. We then study three different domain wall spacetimes dual to zero-temperature states with a broken U(1) symmetry. In these "holographic superconductors", we find features similar to conventional superconductors such as the development of a gap in the fermionic spectra.

Finally, we investigate the question of how bosonic properties, for example susceptibilities, are affected by fermionic properties, such as Fermi surface singularities, in holographic states of matter. We do this by computing the static charge susceptibility in the three-charge black hole state. Our results reveal singularities at complex momenta, with a real part approximately equal to the largest Fermi momentum in the state.

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