A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
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Kluth,Fixed points of quantum gravity from dimen- sional regularization, Phys
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abstract
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or dimensionful couplings. By construction, this setup respects global and gauge symmetries, including diffeomorphisms, and allows for systematic extensions to higher loop orders. We exemplify this approach in the context of four-dimensional quantum gravity. By computing one-loop $\beta$-functions, we find a non-trivial fixed point. It shows two real critical exponents and is compatible with Weinberg's asymptotic safety scenario. Moreover, the underlying structure of divergences suggests that gravity becomes, effectively, two-dimensional in the ultraviolet. We discuss the significance of our results as well as further applications and extensions to higher loop orders.
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background 5representative citing papers
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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.
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
Functional dimensional regularization applied to the O(N) universality class yields critical exponents comparable to advanced non-perturbative methods while retaining efficiency and rapid convergence.
A mass-dependent renormalization scheme from dimensional regularization yields smooth threshold transitions in QCD and implements the Appelquist-Carazzone theorem by reducing to minimal subtraction at high energies.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
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The perturbative Ricci flow in gravity
A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
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A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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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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Spectral Functions of Lorentzian Quantum Gravity
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
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Functional Dimensional Regularization for O(N) Models
Functional dimensional regularization applied to the O(N) universality class yields critical exponents comparable to advanced non-perturbative methods while retaining efficiency and rapid convergence.
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Smooth Threshold Effects from Dimensional Regularization
A mass-dependent renormalization scheme from dimensional regularization yields smooth threshold transitions in QCD and implements the Appelquist-Carazzone theorem by reducing to minimal subtraction at high energies.
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Asymptotically safe quantum gravity and its phenomenology -- a review
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.