Math 2.0

Relativity and gravitational theory Quantum gravity Conjecture

Asymptotic safety in quantum gravity

Builds on Renormalization groupFixed point of the renormalization groupEinstein–Hilbert actionQuantum field theory

Statement

Consider the space of dimensionless couplings of all diffeomorphism-invariant actions for the metric, with the flow of the renormalization group. The asymptotic safety conjecture states that:

  1. this flow has a non-Gaussian fixed point, that is, a fixed point at which not all couplings vanish;
  2. the set of trajectories that reach this fixed point in the ultraviolet limit (its ultraviolet critical surface) has finite dimension;
  3. the physical theory of quantum gravity is one of these trajectories.

Then the quantum field theory of gravity is predictive at all energies, although it is not perturbatively renormalizable.

Remarks

Steven Weinberg proposed the scenario in 1976 as an alternative to perturbative renormalizability, which fails for gravity. In 2+ε2 + \varepsilon dimensions, perturbation theory in ε\varepsilon finds such a fixed point. In four dimensions, the evidence comes from the functional renormalization group, introduced for gravity by Martin Reuter in the 1990s. Truncations of the effective action, starting with the Einstein–Hilbert action with cosmological constant, show a non-Gaussian fixed point. This fixed point has a small number of relevant directions. These results depend on truncations, and the conjecture is open.

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  1. Einstein–Hilbert action concept
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  3. Quantum field theory concept
  4. Renormalization group concept
  5. Asymptotic safety in quantum gravity conjecture

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Further reading

  1. Web https://en.wikipedia.org/wiki/Asymptotic_safety
About this page
TagJ02PA86B38
URIm2://J02PA86B38
Kindconjecture
WritingW0 stub
MSC83C45, 81T17, 81T16
StatusThis copy of the site has no build data. Run m2 status J02PA86B38.
AboutRenormalization group
UsesRenormalization group, Fixed point of the renormalization group, Einstein–Hilbert action, Quantum field theory
Changed3 November 2026

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