In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
Ambjørn, J
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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.
fields
hep-th 3years
2026 3representative citing papers
Causal Dynamical Triangulations regularizes the gravitational path integral via causal triangulations, enabling Monte Carlo simulations that produce an emergent de Sitter universe with short-distance spectral dimension near 2 and evidence for an ultraviolet fixed point.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
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Towards gauge independence in asymptotically safe quantum gravity
In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
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Causal Dynamical Triangulations: New Lattice Theory of Quantum Gravity
Causal Dynamical Triangulations regularizes the gravitational path integral via causal triangulations, enabling Monte Carlo simulations that produce an emergent de Sitter universe with short-distance spectral dimension near 2 and evidence for an ultraviolet fixed point.
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Asymptotically safe quantum gravity and its phenomenology -- a review
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