A spectral cutoff RG flow on S^3 realizes the Wilson-Fisher universality class with one relevant direction and critical exponents close to flat-space values.
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The Exact Renormalisation Group and Approximate Solutions
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abstract
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\lambda \varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
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representative citing papers
A non-trivial UV fixed point for the scalar matter form factor exists in asymptotically safe quantum gravity, with a discrete spectrum of critical exponents and infrared locality restored.
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.
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.
Asymptotically safe gravitational form factors are obtained by integrating the proper-time flow to k=0; finite cutoff-independent results with 1/q² UV decay require selecting the non-Gaussian fixed point as UV boundary condition.
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.
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
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.
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
Renormalization group improved unimodular black holes with self-consistent radial scale identification yield non-singular metrics and associated mass gaps.
A Legendre transform establishes an exact duality between the classical Polchinski equation and the authors' classical RG equation for the gravitational effective action.
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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.
Lecture notes on defining scalar QFTs and assigning geometric structure to the space of possible theories.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
citing papers explorer
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Coarse graining from within: Wilson-Fisher universality on $S^3$
A spectral cutoff RG flow on S^3 realizes the Wilson-Fisher universality class with one relevant direction and critical exponents close to flat-space values.
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Scaling Solutions of Matter Form Factors in Asymptotically Safe Quantum Gravity
A non-trivial UV fixed point for the scalar matter form factor exists in asymptotically safe quantum gravity, with a discrete spectrum of critical exponents and infrared locality restored.
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Rethinking Dimensional Regularization in Critical Phenomena
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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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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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.
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Asymptotically Safe Gravitational Form Factors from the Proper-Time Flow Equation
Asymptotically safe gravitational form factors are obtained by integrating the proper-time flow to k=0; finite cutoff-independent results with 1/q² UV decay require selecting the non-Gaussian fixed point as UV boundary condition.
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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.
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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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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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Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
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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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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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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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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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Scalar Quantum Fields: Theory Space and its Geometry
Lecture notes on defining scalar QFTs and assigning geometric structure to the space of possible theories.
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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.