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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Exact evolution equation for the effective potential
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abstract
We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories with massless modes in less than four dimensions which are relevant for the high temperature phase transition in particle physics or the computation of critical exponents in statistical mechanics.
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representative citing papers
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
Surface fRG extension shows d-wave superconductivity from the 2D Hubbard model persists across most interlayer couplings but splits into two regimes separated by a narrow region of incommensurate spin-density-wave and spin-bond order at intermediate couplings.
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.
A first-principles FRG approach to two-flavor QCD derives low-energy constants for the pion, sigma-meson and scalar diquark without parameters beyond QCD itself, including new diquark properties for color-superconducting models.
Starobinsky inflation rules out two of three non-Gaussian fixed points in asymptotically safe scalar-tensor theories, identifying viable RG trajectories from the remaining 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.
FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.
Auxiliary tensor fields in composite gravity models acquire dynamical kinetic terms via FRG flows, reproducing the transverse-traceless quadratic Einstein-Hilbert structure in the spin-2 sector.
A coupled DSE-FRG-holographic model predicts the QCD critical end point at T_CEP approximately 130-135 MeV and mu_B,CEP approximately 600 MeV, with sensitivity to regulator and normalization choices.
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
Operator PIRGs complete the prior PIRG method by enabling computation of all correlation functions, demonstrated analytically in zero-dimensional phi^4 theory via vertex expansion to ten-point functions.
In asymptotically safe gravity, radiation-filled Bianchi-I cosmologies show quantum corrections that soften anisotropy, while magnetic fields lead to persistent Kasner anisotropy without Lambda but isotropic de Sitter decay with nonzero Lambda.
A coupling α is identified with de Sitter entropy via holography and RG flow; imposing monotonic infrared increase on α(k) yields the observed cosmological constant value.
Analytical approximation to the graviton propagator from Asymptotic Safety shows no extra poles and identifies a mechanism where spurious pole residues vanish at higher orders.
Renormalization group improved unimodular black holes with self-consistent radial scale identification yield non-singular metrics and associated mass gaps.
fRG calculations show the jet quenching parameter hat q is enhanced above the chiral boundary and peaks near the QCD critical end point due to critical sigma fluctuations.
The symmetry-improved CJT formalism yields stable global thermodynamic quantities across different pressure prescriptions in the three-flavor linear sigma model, with quantitative differences near the chiral transition.
A Legendre transform establishes an exact duality between the classical Polchinski equation and the authors' classical RG equation for the gravitational effective action.
Including mesonic fluctuations beyond mean field in the quark-meson-diquark model substantially modifies the phase structure, with diquark condensation dominating at strong couplings as revealed by pole masses and the Silver-Blaze property.
FRG analysis in the linear sigma model for QC2D shows enhanced meson U(1)_A anomaly couplings with increasing mu_q but suppressed topological susceptibility following chiral restoration at high density or temperature.
FRG study of QCD-like theories finds the CP-violating four-fermion operator becomes relevant in the chirally broken phase when the gauge coupling runs, while finite quark mass strongly suppresses infrared running of the theta parameter.
The paper claims an FRG derivation of emergent AdS geometry for the O(N) vector model, but the derivation's key step contradicts its own equations.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
citing papers explorer
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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.
-
Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
-
Surface Functional Renormalization Group for Layered Quantum Materials
Surface fRG extension shows d-wave superconductivity from the 2D Hubbard model persists across most interlayer couplings but splits into two regimes separated by a narrow region of incommensurate spin-density-wave and spin-bond order at intermediate couplings.
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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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Scalar diquarks in the QCD vacuum
A first-principles FRG approach to two-flavor QCD derives low-energy constants for the pion, sigma-meson and scalar diquark without parameters beyond QCD itself, including new diquark properties for color-superconducting models.
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Starobinsky-inflation in asymptotically safe shift-symmetric scalar-tensor theory
Starobinsky inflation rules out two of three non-Gaussian fixed points in asymptotically safe scalar-tensor theories, identifying viable RG trajectories from the remaining 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.
-
FunKit: A computer algebra toolkit for functional approaches
FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.
-
Emergence of dynamical tensor fields in composite models of gravity
Auxiliary tensor fields in composite gravity models acquire dynamical kinetic terms via FRG flows, reproducing the transverse-traceless quadratic Einstein-Hilbert structure in the spin-2 sector.
-
Unified Functional-Holographic Theory of the QCD Critical End Point
A coupled DSE-FRG-holographic model predicts the QCD critical end point at T_CEP approximately 130-135 MeV and mu_B,CEP approximately 600 MeV, with sensitivity to regulator and normalization choices.
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Towards theory constraints on ultralight dark matter from quantum gravity
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
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Physics-informed operator flows and observables
Operator PIRGs complete the prior PIRG method by enabling computation of all correlation functions, demonstrated analytically in zero-dimensional phi^4 theory via vertex expansion to ten-point functions.
-
Bianchi-I Cosmology with Radiation in Asymptotically Safe Gravity
In asymptotically safe gravity, radiation-filled Bianchi-I cosmologies show quantum corrections that soften anisotropy, while magnetic fields lead to persistent Kasner anisotropy without Lambda but isotropic de Sitter decay with nonzero Lambda.
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Microscopic entropy of de Sitter spacetime and entropic solution to the old cosmological constant problem
A coupling α is identified with de Sitter entropy via holography and RG flow; imposing monotonic infrared increase on α(k) yields the observed cosmological constant value.
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The pole truth: an analytical graviton propagator from Asymptotic Safety
Analytical approximation to the graviton propagator from Asymptotic Safety shows no extra poles and identifies a mechanism where spurious pole residues vanish at higher orders.
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Improved unimodular black holes with self-consistent renormalization scale identification
Renormalization group improved unimodular black holes with self-consistent radial scale identification yield non-singular metrics and associated mass gaps.
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Functional renormalization group study of the jet quenching parameter near the QCD critical end point
fRG calculations show the jet quenching parameter hat q is enhanced above the chiral boundary and peaks near the QCD critical end point due to critical sigma fluctuations.
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Thermodynamics in symmetry-improved Cornwall-Jackiw-Tomboulis formalism: application to the low-energy effective theory of QCD
The symmetry-improved CJT formalism yields stable global thermodynamic quantities across different pressure prescriptions in the three-flavor linear sigma model, with quantitative differences near the chiral transition.
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Classical Renormalization Group Equations for General Relativity
A Legendre transform establishes an exact duality between the classical Polchinski equation and the authors' classical RG equation for the gravitational effective action.
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Diquark Correlators and Phase Structure in the Quark-Meson-Diquark Model beyond Mean Field
Including mesonic fluctuations beyond mean field in the quark-meson-diquark model substantially modifies the phase structure, with diquark condensation dominating at strong couplings as revealed by pole masses and the Silver-Blaze property.
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FRG analysis of dense two-color QCD within the linear sigma model
FRG analysis in the linear sigma model for QC2D shows enhanced meson U(1)_A anomaly couplings with increasing mu_q but suppressed topological susceptibility following chiral restoration at high density or temperature.
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$CP$ phase structure of QCD from functional renormalization group
FRG study of QCD-like theories finds the CP-violating four-fermion operator becomes relevant in the chirally broken phase when the gauge coupling runs, while finite quark mass strongly suppresses infrared running of the theta parameter.
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Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group via Bulk Metric Reconstruction
The paper claims an FRG derivation of emergent AdS geometry for the O(N) vector model, but the derivation's key step contradicts its own equations.
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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.