PIRSA:20110036

Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry

APA

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}}
          }
          

Bianca Dittrich Perimeter Institute for Theoretical Physics

Abstract

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.