The nonperturbative functional renormalization group and its applications

Abstract

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.

v3) Review article, 93 pages + bibliography, 35 figures

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• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• On the complex structure of Yang-Mills theory
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Structural aspects of FRG in quantum tunnelling computations
• The two upper critical dimensions of the Ising and Potts models
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Towards background field independence within the Gribov horizon
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• QFT without infinities and hierarchy problem
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Anomalous Collective Dynamics of Auto-Chemotactic Populations
• Interaction-driven first-order and higher-order topological superconductivity
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model
• A Lorentzian renormalisation group equation for gauge theories
• QCD phase transition and equation of state of stellar strong interaction matter via Dyson-Schwinger equation approach
• Chiral symmetry breaking in accelerating and rotating frames
• Functional renormalization for repulsive Bose-Bose mixtures at zero temperature
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Lectures in Quantum Gravity
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• A comprehensive approach to the physics of mesons
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Flowing bosonization in the nonperturbative functional renormalization-group approach
• Real-time observables from Euclidean thermal correlation functions
• Many-body forces and nucleon clustering near the QCD critical point
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• Stochastic dynamics for Group Field Theories
• Universality of pseudo-Goldstone damping near critical points
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Ghost-gluon vertex in the presence of the Gribov horizon: General kinematics
• Magic angle of Sr${}_2$RuO${}_4$: Optimizing correlation-driven superconductivity
• Hubble selection of the weak scale from QCD quantum critical point
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Spin-valley magnetism on the triangular moiré lattice with SU(4) breaking interactions
• A correspondence between the free and interacting field theories
• Functional renormalisation group approach to shell models of turbulence
• Universal scaling in real dimension
• Universal and non-universal large deviations in critical systems
• Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• On the phase structure of extra-dimensional gauge theories with fermions
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Vector interaction bounds in NJL-like models from LQCD estimated curvature of the chiral crossover line
• Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension
• Momentum-dependent quasiparticle properties of the Fermi polaron from the functional renormalization group
• Non-perturbative quantum Galileon in the exact renormalization group
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Spectral properties and observables in ultracold Fermi gases
• Suppression of proton decay in quantum gravity
• Exact renormalization group for wave functionals
• Scaling solutions for asymptotically free quantum gravity
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• Construction of energy density functional for arbitrary spin polarization using functional renormalization group
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• A Rigorous Derivation of the Functional Renormalisation Group Equation
• $\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides
• Mass-dependence of pseudocritical temperature in mean field approximation
• Determining wave equations in holographic QCD from Wilsonian renormalization group
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion
• Physics-informed neural networks for solving functional renormalization group on a lattice
• Dynamical symmetry breaking in Georgi-Glashow chiral-gauge theories
• Functional renormalisation group approach to the finite-temperature Bose polaron
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Functional Renormalisation Group for Brownian Motion I: The Effective Equations of Motion
• The quantum criticality of the Standard Model and the hierarchy problem
• Generalized Hertz action and quantum criticality of two-dimensional Fermi systems
• Vacuum Energy and Renormalization of the Field-Independent Term
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• New renormalization group study of the 3-state Potts model and related statistical models
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• A Universe from a Lagrangian Fixed Point
• Higher derivative extension of the functional renormalization group
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Renormalization Flow of Nonlinear Electrodynamics
• Speed of sound peak in two-color dense QCD: confronting effective models with lattice data
• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Functional renormalization group for extremely correlated electrons
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
• Cosmological functional renormalisation group, extended Galilean invariance and the sweeping effect
• Exact effective action for the O(N) vector model in the large N limit
• A basis of the gradient flow exact renormalization group for gauge theory
• Nonperturbative treatment of a quenched Langevin field theory
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Dynamical and finite-size effects on the criterion of first-order phase transition
• Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators
• Functional renormalization group for signal detection and stochastic ergodicity breaking
• Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Superfluidity in multicomponent fermions via the functional renormalization group
• Functional renormalization group flows of $\mathcal{N}=1$ supersymmetric abelian gauge model with one chiral and one vector superfield
• Influence of light quark loops on the Wigner phase with Dyson-Schwinger equations approach
• On the running and the UV limit of Wilsonian renormalization group flows
• Universality in the exact renormalization group: comparison to perturbation theory
• Quantum-field multiloop calculations in critical dynamics
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism
• Functional Renormalization Group Approach for Signal Detection
• Universal amplitudes ratios for critical aging via functional renormalization group
• Functional renormalization group for p=2 like glassy matrices in the planar approximation: I. Vertex expansion at equilibrium
• In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Relativistic BEC extracted from a complex FRG flow equation
• Subtleties in the calculation of correlation functions for hot and dense systems
• Time-translation invariance symmetry breaking hidden by finite-scale singularities
• Indications against dynamical CPT symmetry restoration in quantum gravity
• QCD phase transition at finite temperature and chemical potential with the non-extensive statistics
• Physics-informed operator flows and observables
• Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions
• Functional Renormalization Group Flows and Gauge Consistency in QED
• Scaling Behaviors in Active Model B+ via the Functional Renormalization Group
• Explicit construction of the energy-momentum tensor in the large N limit
• Constraint correlation functions of the one-dimensional Ising model in the scaling limit
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Constraint effective action and critical correlation functions at fixed magnetization
• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet
• Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific
• Vertex functions and their flow equations from the 2PI effective action
• The $\theta$-vacuum from functional renormalisation
• Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling
• Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function
• New universality classes govern the critical and multicritical behavior of an active Ising model
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Fate of chiral symmetry in Riemann-Cartan geometry
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Spin functional renormalization group for dimerized quantum spin systems
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Stability of ${\phi }^4$-vector model: four-loop $\epsilon$ expansion study
• Non-Perturbative $S$-matrix Renormalization
• Charting GLOBs in Asymptotically Safe Gravity
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Gribov copies in the quark propagator
• Renormalisation of non-differentiable potentials
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Geodesics in Quantum Gravity
• The phases of QCD reached in terrestrial and cosmic colliders
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Renormalization group approach to the elastic properties of graphene bilayers
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation
• Surface Functional Renormalization Group for Layered Quantum Materials
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group
• Spectral Bifurcations in Quasinormal Modes of Regular BTZ Black Holes
• Basic properties of an alternative flow equation in gravity theories
• The effect of charm quark on the QCD chiral phase diagram
• High-order fluctuations of temperature in hot QCD matter
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases
• Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective
• Functional renormalization group equations for antisymmetric tensor field models at finite temperature
• Functional renormalization group approach to phonon modified criticality: anomalous dimension of strain and non-analytic corrections to Hooke's law
• Spin bond order driven by extended repulsive interactions in doped graphene
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group
• Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures
• Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors
• Exact generating function of a zero-dimensional supersymmetric non-linear sigma model
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes