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 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.
- Publication:
-
Frontiers in Physics
- Pub Date:
- July 2020
- DOI:
- 10.3389/fphy.2020.00247
- arXiv:
- arXiv:2002.01693
- Bibcode:
- 2020FrP.....8..247A
- Keywords:
-
- Quantum Gravity;
- phase transitions;
- causal dynamical triangulations;
- asymptotic safety;
- Lattice field theory;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Lattice