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Annales de l’Institut Henri Poincaré D

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Volume 5, Issue 2, 2018, pp. 173–210
DOI: 10.4171/AIHPD/52

Published online: 2018-06-04

Flowing to the continuum limit in tensor models for quantum gravity

Astrid Eichhorn[1] and Tim Koslowski[2]

(1) University of Heidelberg, Germany
(2) Universidad Nacional Autónoma de México, Ciudad de México, Mexico

Tensor models provide a way to access the path-integral for discretized quantum gravity in $d$ dimensions. As in the case of matrix models for 2-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size $N$ serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for 3-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.

Keywords: Quantum gravity, functional Renormalization Group, tensor model

Eichhorn Astrid, Koslowski Tim: Flowing to the continuum limit in tensor models for quantum gravity. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), 173-210. doi: 10.4171/AIHPD/52