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Asymptotic Safety (Quantum Einstein Gravity) vs Lorentzian Asymptotic Safety

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	Asymptotic Safety (Quantum Einstein Gravity) Frontier	Lorentzian Asymptotic Safety Frontier
Proposed	1979 / 1998	2025
Key figures	Steven Weinberg, Martin Reuter	Frank Saueressig, Jian Wang
In one sentence	Weinberg proposed in 1979 that gravity's ultraviolet behavior is tamed not by extra physics but by a non-trivial fixed point: the gravitational couplings approach a finite value at high energies rather than blowing up. Reuter made the proposal calculable in 1998 by writing down a functional renormalization-group equation that tracks how the couplings flow with energy. The past three decades have been about increasingly realistic checks that the fixed point really exists.	Almost all asymptotic-safety calculations are performed in Euclidean signature (imaginary time), which makes the renormalization-group machinery tractable. Whether the results carry over to the Lorentzian signature of actual physical spacetime is a long-standing open question. Saueressig and Wang's 2025 'foliated' approach derives asymptotic safety directly in Lorentzian signature using an Arnowitt-Deser-Misner decomposition and a controlled Wick rotation.
Predictions	Gravitational couplings approach a non-trivial fixed point at energies near the Planck scale; this is the central testable structural prediction of the framework The theory remains predictive at arbitrarily high energies without needing extra fields or strings; quantum gravity is a self-contained sector Specific dimensionless ratios at the fixed point can be computed (e.g. the product of the cosmological constant and Newton's constant in fixed-point units); these ratios should be consistent across different truncations and matter contents Newtonian gravity is recovered at low energies as the infrared limit of the renormalization-group flow from the fixed point; this is a consistency requirement, not a free prediction	The asymptotic-safety fixed point exists in Lorentzian signature with structure consistent with the Euclidean-signature results; this is the central testable claim of the foliated approach The Wick rotation between Lorentzian and Euclidean asymptotic-safety calculations is controlled and well-defined, at least within the foliated framework; specific saddles and integration contours are tracked explicitly rather than assumed to be benign Causal structure (light cones, the timelike-spacelike distinction) is preserved by the renormalization-group flow in the foliated framework; the concrete check is whether the light-cone structure at the fixed-point couplings matches the low-energy light-cone geometry recovered from the infrared limit of the flow Specific dimensionless ratios at the fixed point in Lorentzian signature should match those from Euclidean calculations within calculational uncertainty; discrepancies would indicate signature dependence that the Euclidean program has missed
Where it breaks	Truncation convergence is unproven (see family-level sharedObjections for full statement). The strongest objection to the program is structural: no proof exists that the truncations converge to the true theory Most calculations are Euclidean; the Lorentzian carry-over is contested (see Lorentzian variant for the active research line attempting to address this) Asymptotic safety has no distinctive low-energy prediction confirmed experimentally beyond the conditional Higgs result, leaving the framework's status similar to other quantum-gravity proposals Some authors (Donoghue 2020 and others) have argued that asymptotic safety as formulated may not survive once non-perturbative effects beyond the renormalization-group truncation are properly included; this is a sharpened form of the truncation-convergence concern	The foliated framework was published in 2025; most consistency checks against Euclidean predictions remain in progress. The full range of asymptotic-safety predictions has not yet been re-derived in Lorentzian signature, so caution is appropriate The foliated approach relies on specific choices: an Arnowitt-Deser-Misner-style decomposition of spacetime, a particular Wick rotation prescription, a choice of foliation surface. Whether the results are independent of these choices, the analog of background independence in the Lorentzian setting, is a technical question still being investigated Some authors have argued that the Lorentzian path integral for gravity is mathematically ill-defined in a deeper sense than the Wick rotation can resolve; if so, even a successful foliated derivation may be sitting on top of a structural problem The variant inherits all the truncation-convergence and BRST-symmetry concerns of the broader asymptotic-safety program; the move to Lorentzian signature does not address those questions
Key unresolved problem	The approximation problem: the key result comes from cutting the equations short to make them solvable, and no one has proven that the full untruncated calculation would settle on the same fixed point rather than wandering off.	The time-slicing problem: the real-time results may hinge on an arbitrary choice of how spacetime is sliced into moments, the ADM foliation, rather than reflecting physics that holds no matter how you slice it.
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Asymptotic Safety (Quantum Einstein Gravity)

1979 / 1998 · Frontier

Lorentzian Asymptotic Safety

2025 · Frontier

Proposed

1979 / 1998

2025

Key figures

Steven Weinberg, Martin Reuter

Frank Saueressig, Jian Wang

In one sentence

Weinberg proposed in 1979 that gravity's ultraviolet behavior is tamed not by extra physics but by a non-trivial fixed point: the gravitational couplings approach a finite value at high energies rather than blowing up. Reuter made the proposal calculable in 1998 by writing down a functional renormalization-group equation that tracks how the couplings flow with energy. The past three decades have been about increasingly realistic checks that the fixed point really exists.

Almost all asymptotic-safety calculations are performed in Euclidean signature (imaginary time), which makes the renormalization-group machinery tractable. Whether the results carry over to the Lorentzian signature of actual physical spacetime is a long-standing open question. Saueressig and Wang's 2025 'foliated' approach derives asymptotic safety directly in Lorentzian signature using an Arnowitt-Deser-Misner decomposition and a controlled Wick rotation.

Predictions

Gravitational couplings approach a non-trivial fixed point at energies near the Planck scale; this is the central testable structural prediction of the framework
The theory remains predictive at arbitrarily high energies without needing extra fields or strings; quantum gravity is a self-contained sector
Specific dimensionless ratios at the fixed point can be computed (e.g. the product of the cosmological constant and Newton's constant in fixed-point units); these ratios should be consistent across different truncations and matter contents
Newtonian gravity is recovered at low energies as the infrared limit of the renormalization-group flow from the fixed point; this is a consistency requirement, not a free prediction

The asymptotic-safety fixed point exists in Lorentzian signature with structure consistent with the Euclidean-signature results; this is the central testable claim of the foliated approach
The Wick rotation between Lorentzian and Euclidean asymptotic-safety calculations is controlled and well-defined, at least within the foliated framework; specific saddles and integration contours are tracked explicitly rather than assumed to be benign
Causal structure (light cones, the timelike-spacelike distinction) is preserved by the renormalization-group flow in the foliated framework; the concrete check is whether the light-cone structure at the fixed-point couplings matches the low-energy light-cone geometry recovered from the infrared limit of the flow
Specific dimensionless ratios at the fixed point in Lorentzian signature should match those from Euclidean calculations within calculational uncertainty; discrepancies would indicate signature dependence that the Euclidean program has missed

Where it breaks

Truncation convergence is unproven (see family-level sharedObjections for full statement). The strongest objection to the program is structural: no proof exists that the truncations converge to the true theory
Most calculations are Euclidean; the Lorentzian carry-over is contested (see Lorentzian variant for the active research line attempting to address this)
Asymptotic safety has no distinctive low-energy prediction confirmed experimentally beyond the conditional Higgs result, leaving the framework's status similar to other quantum-gravity proposals
Some authors (Donoghue 2020 and others) have argued that asymptotic safety as formulated may not survive once non-perturbative effects beyond the renormalization-group truncation are properly included; this is a sharpened form of the truncation-convergence concern

The foliated framework was published in 2025; most consistency checks against Euclidean predictions remain in progress. The full range of asymptotic-safety predictions has not yet been re-derived in Lorentzian signature, so caution is appropriate
The foliated approach relies on specific choices: an Arnowitt-Deser-Misner-style decomposition of spacetime, a particular Wick rotation prescription, a choice of foliation surface. Whether the results are independent of these choices, the analog of background independence in the Lorentzian setting, is a technical question still being investigated
Some authors have argued that the Lorentzian path integral for gravity is mathematically ill-defined in a deeper sense than the Wick rotation can resolve; if so, even a successful foliated derivation may be sitting on top of a structural problem
The variant inherits all the truncation-convergence and BRST-symmetry concerns of the broader asymptotic-safety program; the move to Lorentzian signature does not address those questions

Key unresolved problem

The approximation problem: the key result comes from cutting the equations short to make them solvable, and no one has proven that the full untruncated calculation would settle on the same fixed point rather than wandering off.

The time-slicing problem: the real-time results may hinge on an arbitrary choice of how spacetime is sliced into moments, the ADM foliation, rather than reflecting physics that holds no matter how you slice it.

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