UBC Theses and Dissertations
Holographic entanglement entropy : structure and applications from noncommutative field theories to energy conditions Rabideau, Charles
The holographic Ryu-Takayanagi formula for entanglement entropy connects the entanglement of a field theory to the geometry of a dual gravitational theory in a straightforward and universal way. The first part of this thesis applies this formula to study the entanglement entropy in strongly coupled noncommutative field theories. It is found that the ground state of these theories have substantial entanglement at the length scale of the noncommutativity. The entanglement entropy in a different perturbative regime is also computed, where in contrast it is found that noncommutative interactions do not induce long range entanglement in the ground state to leading order in perturbations theory. The second part of this thesis explores some general consequences of this holographic formula for the entanglement entropy. Identities involving entanglement entropies are related to nontrivial geometric constraints on gravitational duals. In particular, the strong subadditivity of entanglement entropy is used to show that dual three dimensional asymptotically anti-de Sitter gravitational states must obey an averaged null energy condition. Finally, this holographic formula allows us at least in principle to express the entanglement entropy of a region in a holographic field theory in terms of the one-point functions in that theory. This is explored in the context of a two dimensional conformal field theory where explicit calculations are possible. Our results in this case allow us to extend a recent proposal that the entanglement entropy of states near the vacuum of conformal theories can be understood by propagation in an auxiliary de Sitter space.
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