Renormalization procedure for random tensor networks and the canonical tensor model

TL;DR

This paper introduces a renormalization procedure for random tensor networks, linking the flow to the canonical tensor model, a discretized quantum gravity model, and explores phase transition relations.

Contribution

It generalizes previous work by connecting the renormalization-group flow of random tensor networks to the Hamiltonian vector flow of the canonical tensor model.

Findings

Flow corresponds to Hamiltonian vector flow of the canonical tensor model

Established relation between phase transitions and flow discontinuities

Extended previous results from N=2 to general cases

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.