Thesis: Tensor networks for dynamic spacetimes

TL;DR

This thesis explores extending tensor network models to describe dynamic spacetimes in AdS/CFT, moving beyond static models to better capture the geometry of evolving universes.

Contribution

It proposes modifications to holographic tensor network models to incorporate features of dynamic spacetimes in AdS/CFT.

Findings

Proposed tensor network modifications for dynamic geometries

Reviewed tensor networks in AdS/CFT context

Connected tensor networks with evolving spacetime geometries

Abstract

Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network - AdS/CFT connection is the association of a graph geometry with the tensor network. In the context of the AdS/CFT correspondence tensor network models have so far been limited to describing static spacetimes. In this thesis we look to extend tensor network models of AdS/CFT by describing the geometry of a dynamic spacetime using a tensor network. We provide a review of tensor networks in the context of AdS/CFT to motivate this extension, before proposing modifications of holographic tensor network models that capture features of AdS/CFT with dynamic spacetimes. This thesis includes the results of arXiv submission 1611.06220, along with a review of the relevant literature.