Random Tensors and Quantum Gravity

TL;DR

This paper introduces tensor field theories with a focus on their relevance to quantum gravity, highlighting how asymptotic freedom supports a form of 'quantum relativity' in the ultraviolet regime.

Contribution

It provides an informal overview of tensor field theories and their renormalization group, emphasizing conceptual motivations from quantum gravity rather than technical details.

Findings

Tensor field theories exhibit asymptotic freedom.

Asymptotic freedom supports a 'quantum relativity' principle.

Physics in the ultraviolet becomes basis-independent.

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.