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The nonperturbative functional renormalization group and its applications
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The nonperturbative functional renormalization group and its applications
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The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.
Forward citations
Cited by 30 Pith papers
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Pion Distribution Amplitudes from Functional QCD
fRG-based functional QCD plus LaMET yields a saturated pion quasi-DA at Pz=4.5 GeV and a second moment ⟨ξ²⟩π=0.267, smaller than lattice-LaMET and consistent with other nonperturbative methods.
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Pion Distribution Amplitudes from Functional QCD
The pion DA computed from functional QCD via LaMET has ⟨ξ²⟩_π = 0.267 (no quoted error), consistent with sum rules and DSE/BSE and 0.8σ below the lattice-LaMET value 0.300(41).
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Scalar diquarks in the QCD vacuum
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The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors
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Hard cutoff and gauge theories
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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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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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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...
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Kaon Distribution Amplitudes from Euclidean Functional QCD
Kaon DA is single-peaked and asymmetric with moments ⟨ξ⟩_K = 0.020(3) and ⟨ξ²⟩_K = 0.253(12) after 1/P_z² and 1/P_z⁴ extrapolation of the quasi-DA.
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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.
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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 de...
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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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The effect of charm quark on the QCD chiral phase diagram
Adding a dynamical charm quark moves the predicted QCD critical endpoint from (102.9 MeV, 618.8 MeV) to (104.3 MeV, 600.1 MeV).
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Functional renormalization group equations for antisymmetric tensor field models at finite temperature
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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.
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