AUTHOR=Ambjorn Jan , Gizbert-Studnicki Jakub , Görlich Andrzej , Jurkiewicz Jerzy , Loll Renate TITLE=Renormalization in Quantum Theories of Geometry JOURNAL=Frontiers in Physics VOLUME=8 YEAR=2020 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00247 DOI=10.3389/fphy.2020.00247 ISSN=2296-424X ABSTRACT=

A hallmark of non-perturbative theories of quantum gravity is the absence of a fixed background geometry, and therefore the absence in a Planckian regime of any notion of length or scale that is defined a priori. This has potentially far-reaching consequences for the application of renormalization group methods à la Wilson, which rely on these notions in a crucial way. We review the status quo of attempts in the Causal Dynamical Triangulations (CDT) approach to quantum gravity to find an ultraviolet fixed point associated with the second-order phase transitions observed in the lattice theory. Measurements of the only invariant correlator currently accessible, that of the total spatial three-volume, has not produced any evidence of such a fixed point. A possible explanation for this result is our incomplete and perhaps naïve understanding of what constitutes an appropriate notion of (quantum) length near the Planck scale.