Gravitational Holography and Tensor Networks: A Quantum Information Perspective (Tata Infosys Lecture 1)

These lectures are intended to give a flavour of ideas from quantum information theory that have helped shed light on our understanding of quantum gravity, especially in the setting of AdS/CFT. In the first lecture, we will discuss random tensor networks as a toy model for holography, and make sharp connections with the gravitational path integral using the idea of fixed-area states. In the second lecture, we will discuss applications of tensor network techniques to holographic systems, especially in the context of understanding multipartite entanglement measures such as the reflected entropy and entanglement negativity. Finally, in the third lecture, we will discuss shortcomings of tensor networks as toy models, especially with regard to time dependence. We will use ideas from quantum information theory such as modular flow to attempt to bridge the gap between tensor networks and holography.