A renormalization procedure for tensor models and scalar-tensor theories of gravity

TL;DR

This paper develops a renormalization method for tensor models of quantum gravity, showing that Gaussian configurations act as attractors and suggesting that their infrared behavior aligns with scalar-tensor theories of gravity.

Contribution

It introduces a renormalization procedure for symmetric tensor models and links their infrared dynamics to scalar-tensor gravitational theories.

Findings

Gaussian configurations are attractors under renormalization

Infrared dynamics resemble scalar-tensor gravity theories

Tensor models can potentially describe emergent spacetime phenomena

Abstract

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.