REVIEW 34 cited by
The Exact Renormalisation Group and Approximate Solutions
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
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.
Forward citations
Cited by 34 Pith papers
-
The fermion sector of the SMEFT from asymptotically safe gravity
In a toy model of one quark generation, asymptotically safe gravity predicts four-fermion SMEFT coefficients are either Planck-scale suppressed or zero, with exceptions only at very large gravitational coupling.
-
Asymptotic behaviour of the derivative expansion in the ERG
The derivative expansion of the exact renormalization group is divergent for generic operators in any dimension, but behaves as an asymptotic series that converges to high order in common applications.
-
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.
-
Renormalization group flows in area-metric gravity
The first renormalization group analysis of area-metric gravity shows shape-mismatching masses grow toward the infrared, parity is not emergent, and the Immirzi parameter flow has fixed points at γ=0 and γ=∞.
-
De Sitter quantum gravity within the covariant Lorentzian approach to asymptotic safety
In the Einstein-Hilbert truncation on de Sitter, the Lorentzian FRG flow exhibits a non-Gaussian UV fixed point for ζ=1/2 and ζ=1 gauges over restricted parameter ranges.
-
Fermions and the Renormalisation Group at Large N
At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.
-
Functional renormalization of QCD in $1 + 1$ dimensions: four-fermion interactions from quark-gluon dynamics
First functional renormalization group study of two-dimensional QCD with a mass-like regulator, producing flow equations for the gauge coupling, quark mass, and a Fierz-complete set of four-fermion interactions.
-
Gauge-Fermion Cartography: from confinement and chiral symmetry breaking to conformality
A non-perturbative fRG calculation charts confinement and chiral symmetry breaking across flavour number and predicts the conformal window boundary at Nf = 9.60 for Nc = 3.
-
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-Gaussia...
-
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.
-
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.
-
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 boundar...
-
Critical and multicritical Lee-Yang fixed points in the local potential approximation
In the local potential approximation, the Lee-Yang fixed point of iφ^3 theory is followed to d=2 with few-percent-accurate scaling dimensions, while multicritical iφ^{2n+1} fixed points annihilate with new non-perturb...
-
Scaling solutions for gauge invariant flow equations in dilaton quantum gravity
Scaling solutions of a gauge-invariant functional flow equation support the dilaton quantum gravity fixed point, with Planck mass ~ φ² at large field and a stable negative kinetial in the infrared.
-
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.
-
Renormalisation Group approach to General Relativity
An exact RG equation for classical gravity is proposed that reproduces the PM expansion and recovers the 1PN two-body action without explicit three-graviton vertices.
-
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.
-
Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity
The existence of an asymptotically safe UV completion for the Abelian gauge coupling is shown to survive simultaneous variations of the regulator and gauge parameters in certain minimal-sensitivity regions.
-
Self-consistent graviton spectral function in Lorentzian quantum gravity
A self-consistent spectral renormalisation group computation yields a positive, normalizable graviton spectral function with a massless pole and a multi-graviton continuum decaying as 1/(λ² log³ λ²).
-
Matter Spectral Functions from Quantum Gravity
Under asymptotically safe quantum gravity, photon and scalar propagators acquire Källén-Lehmann spectral functions that are non-normalizable and change sign in the ultraviolet.
-
Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems
Adding asymptotically safe gravity to the O(N)^3 tensor field theory converts its asymptotic freedom into an interacting fixed point at a non-zero quartic coupling.
-
Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
A two-dimensional Kurganov-Tadmor finite-volume scheme accurately solves FRG flow equations for effective potentials in multi-dimensional field space, benchmarked against exact zero-dimensional path integrals and appl...
-
$e^+ e^- \to \mu^+ \mu^-$ in the Asymptotically Safe Standard Model
Using reconstructed timelike graviton spectral functions, the authors find that the e+e- to mu+mu- cross-section in the asymptotically safe Standard Model falls as 1/s in the ultraviolet and is compatible with unitarity.
-
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.
-
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.
-
Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
Gravity's non-minimal coupling drives the quartic self-coupling of an O(N) scalar to zero at an attractive fixed point, making the broken-phase theory UV-complete and bounding the scalar mass.
-
Fermi scale from quantum gravity scaling solution
The Fermi/Planck ratio is claimed to be predictable from the analyticity of the quantum-gravity scaling solution for the cosmon-Higgs coupling, with numerics showing the coupling flows to a tiny, near-critical value.
-
Non-Perturbative $S$-matrix Renormalization
An exact, polynomial flow equation for the S-matrix generating functional of a scalar field, equivalent to the Polchinski/Wetterich flows under a change of variables, with on-shell extraction at the classical equation...
-
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 de...
-
A new functional RG flow: regulator-sourced 2PI versus average 1PI
For a quartic scalar theory, a regulator-sourced 2PI flow gives faster running of the potential minimum and the cosmological constant, and slightly slower running of the quartic coupling, compared with the standard We...
-
$CP$ 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 t...
-
The inflationary mechanism in Asymptotically Safe Gravity
Departure from the asymptotically safe gravity fixed point generates a plateau inflaton potential with a nearly scale-invariant spectrum, and the Starobinsky model is recovered for critical exponents θ1=θ2=2.
-
Scalar Quantum Fields: Theory Space and its Geometry
Lecture notes on defining scalar QFTs and assigning geometric structure to the space of possible theories.
-
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.
Discussion (0). Continue with ORCID to comment.