Dittrich, B. (2020). Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry. Perimeter Institute. https://pirsa.org/20110036

MLA

Dittrich, Bianca. Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry. Perimeter Institute, Nov. 18, 2020, https://pirsa.org/20110036

BibTex

@misc{ pirsa_20110036,
doi = {10.48660/20110036},
url = {https://pirsa.org/20110036},
author = {Dittrich, Bianca},
keywords = {Quantum Fields and Strings},
language = {en},
title = {Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry},
publisher = {Perimeter Institute},
year = {2020},
month = {nov},
note = {PIRSA:20110036 see, \url{https://pirsa.org}}
}

In contrast to the 4D case, there are well understood theories of quantum gravity for the 3D case. Indeed, 3D general relativity constitutes a topological field theory (of BF or equivalently Chern-Simons type) and can be quantized as such. The resulting quantum theory of gravity offers many interesting lessons for the 4D case.
In this talk I will discuss the quantum theory which results from quantizing 3D gravity as a topological field theory. This will also allow a derivation of a holographic boundary theory, together with a geometric interpretation of the boundary observables.
The resulting structures can be interpreted in terms of tensor networks, which provide states of the boundary theory.
I will explain how a choice of network structure and bond dimensions constitutes a complete gauge fixing of the diffeomorphism symmetry in the gravitational bulk system. The theory provides a consistent set of rules for changing the gauge fixing and with it the tensor network structure. This provides an example of how diffeomorphism symmetry can be realized in a tensor network based framework.
I will close with some remarks on the 4D case and the challenges we face there.