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 (14)

• Critical phenomena in complex networks
• Colored Group Field Theory
• The Tensor Track, III
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Beta functions of $U(1{)}^d$ gauge invariant just renormalizable tensor models
• Canonical tensor models with local time
• Uniqueness of canonical tensor model with local time
• An analysis of the intermediate field theory of $T^4$ tensor model
• Interpreting canonical tensor model in minisuperspace
• Quantum canonical tensor model and an exact wave function
• Physical states in the canonical tensor model from the perspective of random tensor networks
• A canonical rank-three tensor model with a scaling constraint
• Ising model on random networks and the canonical tensor model

Cited by in corpus (7)

• Emergent symmetries in the canonical tensor model
• Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Matter fields in triangle-hinge models
• Emergent classical geometries on boundaries of randomly connected tensor networks
• An $OSp$ extension of Canonical Tensor Model
• Mother canonical tensor model