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arXiv · 2002.01693

Renormalization in quantum theories of geometry

J. Ambjorn·J. Gizbert-Studnicki·A. Goerlich·J. Jurkiewicz·R. Loll
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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.

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J. Ambjorn, J. Gizbert-Studnicki, A. Goerlich, J. Jurkiewicz, R. Loll. 2020-02-05. Renormalization in quantum theories of geometry. https://arxiv.org/abs/2002.01693

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