Tensor Networks and Holographic Spacetime
Abstract
The holographic principle states that the information in a regions is encoded in degrees of freedom living on its boundary. Tensor networks are a promising new approach to under standing how this encoding of quantum information works. Existing tensor network models have explained how holographic spacetimes implement a form of quantum error correction, but most of these models have been toy models rather than actual proposals for how spacetime might work. We will formulate a more local form of the holographic principle, that determines how qubits flow through space. This will be used to liberate the model from any particular choice of boundary conditions, thus allowing us to explore holography in more physically relevant settings. We will also extend tensor network models to dynamical situations, in which fields evolve with time. In gravitational systems time evolution is implemented by a gauge symmetry, i.e. by regarding different moments of time as physically equivalent. Similarly, tensor networks have a large quantity of gauge symmetry, because many different tensor networks give rise to the same boundary state. We will elucidate the relationship between these two types of gauge symmetry, to see if it is possible to reduce dynamics to tensor network equivalence.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 14, 2022
- Source ID
- FA95501910260
Entities
People
- Aron Wall
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Cambridge