Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 069, 17 pages      arXiv:1603.07278      https://doi.org/10.3842/SIGMA.2016.069
Contribution to the Special Issue on Tensor Models, Formalism and Applications

Random Tensors and Quantum Gravity

Vincent Rivasseau
Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris XI, F-91405 Orsay Cedex, France

Received March 23, 2016, in final form July 06, 2016; Published online July 15, 2016

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.

Key words: renormalization; tensor models; quantum gravity.

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