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Matter-Coupled Asymptotic Safety vs Lorentzian Asymptotic Safety

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	Matter-Coupled Asymptotic Safety Frontier	Lorentzian Asymptotic Safety Frontier
Proposed	2010	2025
Key figures	Mikhail Shaposhnikov, Christof Wetterich, Astrid Eichhorn	Frank Saueressig, Jian Wang
In one sentence	If asymptotic safety is real, what constraints does it put on the matter content of the universe? Shaposhnikov and Wetterich showed in 2010 that combining asymptotic safety with the Standard Model's particle content predicts the Higgs boson mass at approximately 126 GeV, made two years before the LHC measured 125.1 GeV. Either the most striking quantitative success of any quantum-gravity proposal or the most striking accident.	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	The Higgs boson mass at approximately 126 GeV, derived from the requirement that the Standard Model is asymptotically safe with gravity included (Shaposhnikov-Wetterich 2010). Matches the LHC measurement of 125.1 GeV within calculational uncertainties The top-quark Yukawa coupling at high energies should approach a specific fixed-point value; the running between current accessible energies and the Planck scale is calculable and can be compared to data Constraints on possible new fermion and [[scalar-field\|scalar fields]] beyond the Standard Model: matter content that destabilises the gravitational fixed point is excluded; this is in principle testable as new searches at the LHC and future colliders constrain Beyond-Standard-Model scenarios [[Dark matter]] candidates with specific couplings: Eichhorn-Pauly 2021 derives constraints on scalar dark-matter portal couplings from asymptotic-safety consistency requirements; these are testable in principle once dark-matter direct-detection experiments reach sufficient sensitivity	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	The Higgs-mass prediction is conditional on no new particles existing between currently accessible energies and the Planck scale (about 14 orders of magnitude in energy). The LHC has not falsified this assumption but cannot prove it. If new physics shows up at any intermediate scale (a Beyond-Standard-Model resonance, a Grand Unified Theory transition, supersymmetric particles), the Higgs prediction is undermined; the empirical success becomes circumstantial rather than constraining The matter-coupled calculations rely on the same truncation framework as the pure-gravity case, inheriting all the convergence concerns. Adding matter operators makes the truncation space larger but does not address the convergence question Different choices of fermion measure, regulator function, and gauge fixing give different intermediate results for the matter-coupled fixed points. The robustness of the Higgs-mass prediction to all these technical choices is a subject of ongoing investigation Asymptotic safety, like other quantum-gravity programs, lacks an experimental verification mechanism distinct from coincidence with known physics; one quantitatively correct prediction across forty years of work is suggestive but not decisive	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 big-if problem: the celebrated Higgs-mass prediction only holds if there is no undiscovered physics across a huge energy gap, fourteen orders of magnitude, an assumption colliders cannot confirm and one new particle would break.	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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Matter-Coupled Asymptotic Safety

2010 · Frontier

Lorentzian Asymptotic Safety

2025 · Frontier

Proposed

2010

2025

Key figures

Mikhail Shaposhnikov, Christof Wetterich, Astrid Eichhorn

Frank Saueressig, Jian Wang

In one sentence

If asymptotic safety is real, what constraints does it put on the matter content of the universe? Shaposhnikov and Wetterich showed in 2010 that combining asymptotic safety with the Standard Model's particle content predicts the Higgs boson mass at approximately 126 GeV, made two years before the LHC measured 125.1 GeV. Either the most striking quantitative success of any quantum-gravity proposal or the most striking accident.

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

The Higgs boson mass at approximately 126 GeV, derived from the requirement that the Standard Model is asymptotically safe with gravity included (Shaposhnikov-Wetterich 2010). Matches the LHC measurement of 125.1 GeV within calculational uncertainties
The top-quark Yukawa coupling at high energies should approach a specific fixed-point value; the running between current accessible energies and the Planck scale is calculable and can be compared to data
Constraints on possible new fermion and [[scalar-field|scalar fields]] beyond the Standard Model: matter content that destabilises the gravitational fixed point is excluded; this is in principle testable as new searches at the LHC and future colliders constrain Beyond-Standard-Model scenarios
[[Dark matter]] candidates with specific couplings: Eichhorn-Pauly 2021 derives constraints on scalar dark-matter portal couplings from asymptotic-safety consistency requirements; these are testable in principle once dark-matter direct-detection experiments reach sufficient sensitivity

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

The Higgs-mass prediction is conditional on no new particles existing between currently accessible energies and the Planck scale (about 14 orders of magnitude in energy). The LHC has not falsified this assumption but cannot prove it. If new physics shows up at any intermediate scale (a Beyond-Standard-Model resonance, a Grand Unified Theory transition, supersymmetric particles), the Higgs prediction is undermined; the empirical success becomes circumstantial rather than constraining
The matter-coupled calculations rely on the same truncation framework as the pure-gravity case, inheriting all the convergence concerns. Adding matter operators makes the truncation space larger but does not address the convergence question
Different choices of fermion measure, regulator function, and gauge fixing give different intermediate results for the matter-coupled fixed points. The robustness of the Higgs-mass prediction to all these technical choices is a subject of ongoing investigation
Asymptotic safety, like other quantum-gravity programs, lacks an experimental verification mechanism distinct from coincidence with known physics; one quantitatively correct prediction across forty years of work is suggestive but not decisive

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 big-if problem: the celebrated Higgs-mass prediction only holds if there is no undiscovered physics across a huge energy gap, fourteen orders of magnitude, an assumption colliders cannot confirm and one new particle would break.

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.

Reader vote

No votes yet