Random Tensors and Quantum Gravity

Abstract

We provide an informal introduction to tensor field theories and to their associated renormalization group. We focus more on the general motivations coming from quantum gravity than on the technical details. In particular we discuss how asymptotic freedom of such tensor field theories gives a concrete example of a natural "quantum relativity" postulate: physics in the deep ultraviolet regime becomes asymptotically more and more independent of any particular choice of Hilbert basis in the space of states of the universe.

Section 6 is essentially reproduced from author's arXiv:1507.04190 for self-contained purpose of the review

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• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Phantom-like dark energy from quantum gravity
• Conformality of $1/N$ corrections in SYK-like models
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
• Holographic maps from quantum gravity states as tensor networks
• Quantum Gravity on the computer: Impressions of a workshop
• Reliability of the local truncations for the random tensor models renormalization group flow
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Surgery in colored tensor models
• Stochastic dynamics for Group Field Theories
• Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations
• Aspects of quantum gravity
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint