Universal critical behavior in tensor models for four-dimensional quantum gravity

TL;DR

This paper investigates four-dimensional tensor models for quantum gravity, identifying a potential continuum limit through background-independent coarse-graining, and finds a fixed point with two relevant directions, suggesting universality and connections to asymptotic safety.

Contribution

It introduces a novel background-independent coarse-graining approach to tensor models, revealing a fixed point with two relevant directions relevant for quantum gravity.

Findings

Identified a fixed point with two relevant directions.

Proposed a continuum limit candidate for 4D tensor models.

Discussed potential links to asymptotic safety in quantum gravity.

Abstract

Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed.