Annales de l’Institut Henri Poincaré D
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Published online: 2018-06-04
Flowing to the continuum limit in tensor models for quantum gravityAstrid Eichhorn and Tim Koslowski (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