The Tensor Theory Space

TL;DR

This paper explores the tensor theory space as a background-independent approach to quantum gravity, defining a renormalization group flow that encompasses all tensor-invariant interactions, extending matrix models and non-commutative field theories.

Contribution

It introduces a framework for the functional renormalization group flow in tensor theory space, broadening the scope beyond Einsteinian gravity and matrix models.

Findings

Defines a Wetterich equation for tensor theory space

Includes all fixed-rank tensor-invariant interactions

Generalizes matrix models and non-commutative field theories

Abstract

The tensor track is a background-independent discretization of quantum gravity which includes a sum over all topologies. We discuss how to define a functional renormalization group flow and the Wetterich equation in the corresponding theory space. This space is different from the Einsteinian theory space of asymptotic safety. It includes all fixed-rank tensor-invariant interactions, hence generalizes matrix models and the (Moyal) non-commutative field theory space.