UBC Theses and Dissertations
Second order relative entropy in holographic theories Schulz-Beach, Jonathon Matthew
Recently, there has been growing recognition that the tools from quantum information theory might be well-suited to studying quantum gravity in the context of the gauge/gravity correspondence. It is exploring this connection that is the main motivation for the work in this thesis. In particular, we focus on holographic field theories which possess classical spacetime duals. The aim is that certain conditions on the classical duals will narrow down the types of field theories that can be holographic. This will give a better understanding of the limitations and robustness of the gauge/gravity correspondence. We do so by computing the canonical energy for general perturbations around anti-de Sitter spacetime, which is dual to quantum Fisher information in the field theory. We go on to prove the positivity of canonical energy and discuss the addition of matter fields. We further show that our result can be interpreted as an interaction between scalar fields living in an auxiliary de Sitter spacetime. We concluded with a summary of progress and future challenges for this program.
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