Renormalization procedure for random tensor networks and the canonical tensor model

Abstract

We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.

23 pages, 5 figures; Comments on first order transitions and discontinuity of RG added, and minor corrections

References in corpus (3)

• Critical phenomena in complex networks
• An analysis of the intermediate field theory of $T^4$ tensor model
• Physical states in the canonical tensor model from the perspective of random tensor networks