# The Functional Renormalization Group Equation as an Approach to the Continuum Limit of Tensor Models for Quantum Gravity

### APA

Koslowski, T. (2019). The Functional Renormalization Group Equation as an Approach to the Continuum Limit of Tensor Models for Quantum Gravity. Perimeter Institute. https://pirsa.org/19050011

### MLA

Koslowski, Tim. The Functional Renormalization Group Equation as an Approach to the Continuum Limit of Tensor Models for Quantum Gravity. Perimeter Institute, May. 02, 2019, https://pirsa.org/19050011

### BibTex

@misc{ pirsa_PIRSA:19050011, doi = {10.48660/19050011}, url = {https://pirsa.org/19050011}, author = {Koslowski, Tim}, keywords = {Quantum Gravity}, language = {en}, title = {The Functional Renormalization Group Equation as an Approach to the Continuum Limit of Tensor Models for Quantum Gravity}, publisher = {Perimeter Institute}, year = {2019}, month = {may}, note = {PIRSA:19050011 see, \url{https://pirsa.org}} }

Tim Koslowski Universidad Nacional Autónoma De Mexico (UNAM)

## Abstract

Tensor Models provide one of the calculationally simplest approaches to defining a partition function for random discrete geometries. The continuum limit of these discrete models then provides a background-independent construction of a partition function of continuum geometry, which are candadates for quantum gravity. The blue-print for this approach is provided by the matrix model approach to two-dimensional quantum gravity. The past ten years have seen a lot of progress using (un)colored tensor models to describe state sums if discrete geometries in more than two dimensions. However, so far one has not yet been able to find a continuum limit of these models that corresponds geometries with more than two continuum dimensions. This problem can be studied systematically using exact renormalization group techniques. In this talk I will report on joint work with Astrid Eichhorn, Antonio Perreira, Joseph Ben Geloun, Daniele Oriti, Johannes Lumma, Alicia Castro and Victor Mu\~noz in this direction. In a separate part of the talk I will explain that the renormalization group is not only a tool to help investigating the continuum limit, but that it in fact also provides a stand-alone approach to quantum gravity. In particular, I will show how scaling relations follow from cylidrical consistency relations.