Renormalization in quantum theories of geometry
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 a 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 naive understanding of what constitutes an appropriate notion of (quantum) length near the Planck scale.
Cite
@article{arxiv.2002.01693,
title = {Renormalization in quantum theories of geometry},
author = {J. Ambjorn and J. Gizbert-Studnicki and A. Goerlich and J. Jurkiewicz and R. Loll},
journal= {arXiv preprint arXiv:2002.01693},
year = {2020}
}