Diffeomorphism invariant tensor networks for 3d gravity
Year: 2025
Type: preprint
Abstract: Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of both problems were addressed in a tensor network discretization of topological field theories (TFT) with finite or compact gauge groups. Here, we extend this work towards gravity by generalizing to gauge groups that are discrete or continuous, compact or non-compact. Applied to $\text{SL}(2,\mathbb{R}) \times \text{SL}(2,\mathbb{R})$ Chern-Simons theory, our construction can be interpreted as building states of three dimensional gravity with a negative cosmological constant. Our tensor networks prepare states that satisfy the constraints of Chern-Simons theory. In metric variables, this implies that the states we construct satisfy the Wheeler-DeWitt equation and momentum constraints, and so are diffeomorphism invariant.
Source: arXiv (Cornell University)
Authors: Balasubramanian, Vijay, Cummings, Charlie
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7092290175
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