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.

arXiv commentv3) Review article, 93 pages + bibliography, 35 figures

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• High-precision estimate of the hydrodynamic radius for self-avoiding walks
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• Large N and the renormalization group
• The Heavy Quark Potential from Wilson's Exact Renormalization Group
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Fluctuation-induced modifications of the phase structure in (2+1)-flavor QCD
• Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• Gluon propagator and three-gluon vertex with dynamical quarks
• Dark Matter meets Quantum Gravity
• Gauge hierarchy problem in asymptotically safe gravity--the resurgence mechanism
• Fluctuations and the axial anomaly with three quark flavors
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Invitation to Random Tensors
• Shadow and deflection angle of rotating black hole in asymptotically safe gravity
• Nonminimal hints for asymptotic safety
• Baryon effects on the location of QCD's critical end point
• Hadronization conditions in relativistic nuclear collisions and the QCD pseudo-critical line
• Correlation functions on a curved background
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Anomalous fluctuations in phases with a broken continuous symmetry
• From renormalization group flows to cosmology
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Non-perturbative finite-temperature Yang-Mills theory
• Large-n Critical Behavior of O(n)xO(m) Spin Models
• Two loop results from one loop computations and non perturbative solutions of exact evolution equations
• Inflationary solutions in asymptotically safe f(R) theories
• Critical equation of state from the average action
• Background independence in a background dependent renormalization group
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• A renormalization group approach to time dependent transport through correlated quantum dots
• Critical behavior of Dirac fermions from perturbative renormalization
• Functional renormalization with fermions and tetrads
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• The Higgs Mass and the Scale of New Physics
• Dynamical crossovers in prethermal critical states
• FormTracer - A Mathematica Tracing Package Using FORM
• UV fixed-point structure of the three-dimensional Thirring model
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Functional renormalization group for Luttinger liquids with impurities
• Non-perturbative thermal flows and resummations
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Fixed-Point Structure of Scalar Fields
• On the relevance of matter and glue dynamics for baryon number fluctuations
• Conformally reduced quantum gravity revisited
• Superconductivity in the two-dimensional $t$-$t^{\prime }$-Hubbard model
• Rapidly Converging Truncation Scheme of the Exact Renormalization Group
• Discretization effects on renormalized gauge-field Green's functions, scale setting and gluon mass
• Chiral Susceptibility in (2+1)-flavour QCD
• Towards the determination of the dimension of the critical surface in asymptotically safe gravity
• Transition Temperature of a Uniform Imperfect Bose Gas
• Phase diagram and thermal properties of strong-interaction matter
• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Quantum Improved Schwarzschild-(A)dS and Kerr-(A)dS Space-times
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Particle-hole fluctuations in the BCS-BEC Crossover
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Variable Planck mass from the gauge invariant flow equation
• Critical behavior of the (2+1)-dimensional Thirring model
• Pairing in Many-Fermion Systems: An Exact Renormalisation Group Treatment
• Gauges and functional measures in quantum gravity I: Einstein theory
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Functional renormalization group study of the interacting resonant level model in and out of equilibrium
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• A junction of three quantum wires: restoring time-reversal symmetry by interaction
• On the Functional Renormalization Group approach for Yang-Mills fields
• Volume and Quark Mass Dependence of the Chiral Phase Transition
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Critical exponents of O(N) models in fractional dimensions
• How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Asymptotically Safe Starobinsky Inflation
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Ultracold atoms and the Functional Renormalization Group
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Non-perturbative Approach to Critical Dynamics
• Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System
• Scaling solutions for Dilaton Quantum Gravity
• Fixed Points of Nonlinear Sigma Models in d>2
• Thermoelectric transport in the topological phase due to the coexistence of superconductivity and spin-density-wave
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• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Hořava gravity is asymptotically free (in 2+1 dimensions)
• Impact of topology in foliated Quantum Einstein Gravity
• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Asymptotically Safe Cosmology
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Functional Renormalization Group Approach for Tensorial Group Field Theory: A Rank-6 Model with Closure Constraint
• The Large N Limit and the High Temperature Phase Transition for the ϕ^4 Theory
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm
• Beyond Miransky Scaling
• Background independent exact renormalization group for conformally reduced gravity
• Quark propagator with two flavors of O(a)-improved Wilson fermions
• Asymptotically Safe Standard Model via Vector-Like Fermions
• Hybrid and quark star matter based on a non-perturbative equation of state
• Chiral transitions in three-dimensional magnets and higher order ε-expansion
• Introduction to the nonequilibrium functional renormalization group
• Wicked metrics
• Optimization of Renormalization Group Flow
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• Dynamical structure factors and excitation modes of the bilayer Heisenberg model
• Ising and Gross-Neveu model in next-to-leading order
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Dynamical mean-field theory for bosons
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Connections and geodesics in the space of metrics
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
• An effective action for asymptotically safe gravity
• Analytic continuation of functional renormalization group equations
• Running boundary actions, Asymptotic Safety, and black hole thermodynamics
• Renormalization Group Flow of the Holst Action
• Infrared Behavior of Interacting Bosons at Zero Temperature
• The low-temperature behavior of the quark-meson model
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Four-point functions and the permutation group S4
• Effective action and density functional theory
• Consistency of matter models with asymptotically safe quantum gravity
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Baryon number fluctuations in chiral effective models and their phenomenological implications
• The background scale Ward identity in quantum gravity
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Improving the Renormalization Group approach to the quantum-mechanical double well potential
• A gauge invariant exact renormalization group II
• Functional renormalization group approach to the sine-Gordon model
• Universality and the Renormalisation Group
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• On the Convergence of the Expansion of Renormalization Group Flow Equation
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
• Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering
• Polyakov-Quark-Meson-Diquark Model for two-color QCD
• Solutions to the reconstruction problem in asymptotic safety
• Solving functional flow equations with pseudo-spectral methods
• Correlation functions of three-dimensional Yang-Mills theory from the FRG
• Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Lorentz invariance violations in the interplay of quantum gravity with matter
• Lorentz symmetry is relevant
• Finite temperature spectral functions in the O(N)-model
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
• Transmission Probability for Interacting Electrons Connected to Reservoirs
• On the Fixed-Point Structure of Scalar Fields
• Functional renormalization group approach to the BCS-BEC crossover
• Linking the Quark Meson Model with QCD at High Temperature
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Multi-meson Yukawa interactions at criticality
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Gravitational collapse in Quantum Einstein Gravity
• A Consistent Calculation of Bubble-Nucleation Rates
• Flow equations for spectral functions at finite external momenta
• Asymptotic solutions in asymptotic safety
• Fierz-complete NJL model study: fixed points and phase structure at finite temperature and density
• Multicritical behavior in models with two competing order parameters
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Coarse graining and first order phase transitions
• Quantum-gravity predictions for the fine-structure constant
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Asymptotic safety of simple Yukawa systems
• Functional renormalization for Bose-Einstein Condensation
• Asymptotic freedom in Horava-Lifshitz gravity
• Competing order in correlated electron systems made simple: Consistent fusion of functional renormalization and mean-field theory
• The Price of an Exact, Gauge-Invariant RG-Flow Equation
• Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Functional renormalization for quantum phase transitions with non-relativistic bosons
• Volume Dependence of the Pion Mass in the Quark-Meson-Model
• Hadron Resonance Gas Model with Induced Surface Tension
• Inflation in an effective gravitational model & asymptotic safety
• Singularity-free gravitational collapse and asymptotic safety
• Fluctuations and isentropes near the chiral critical endpoint
• Criticality of Spin Systems with Weak Long-Range Interactions
• Universal thermodynamics of a two-dimensional Bose gas
• Aspect-ratio dependence of thermodynamic Casimir forces
• XY frustrated systems: continuous exponents in discontinuous phase transitions
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Renormalization of the Topological Charge in Yang-Mills Theory
• Far-from-equilibrium quantum many-body dynamics
• Fermions in gravity with local spin-base invariance
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Mass sensitivity of the three-flavor chiral phase transition
• A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
• Probing Baryogenesis through the Higgs Self-Coupling
• Constraints on Hořava gravity from binary black hole observations
• Asymptotic Safety, Emergence and Minimal Length
• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
• On the physical mechanism underlying Asymptotic Safety
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Bose-Einstein condensation of interacting gases
• Self-energy and critical temperature of weakly interacting bosons
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• The phase structure of QCD for heavy quarks
• Asymptotic safety, string theory and the weak gravity conjecture
• Convergence of derivative expansions of the renormalization group
• Nonrelativistic inverse square potential, scale anomaly, and complex extension
• Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology
• The conductance of interacting nano-wires
• Scaling laws near the conformal window of many-flavor QCD
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Spectral function and quasi-particle damping of interacting bosons in two dimensions
• Chiral Mirror-Baryon-Meson Model and Nuclear Matter beyond Mean-Field
• Scaling Solutions in Continuous Dimension
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Equivalence of Local Potential Approximations
• On avoiding Ostrogradski instabilities within Asymptotic Safety
• Equation of state and coarse grained free energy for matrix models
• Manifestly Gauge Invariant QCD
• Polchinski equation, reparameterization invariance and the derivative expansion
• Correlated starting points for the functional renormalization group
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Persistent currents in mesoscopic rings: A numerical and renormalization group study
• Lee-Yang model from the functional renormalization group
• Thermodynamics of QCD low-energy models and the derivative expansion of the effective action
• The Spectrum of the 2+1 Dimensional Gauge Ising Model
• Cosmic Censorship in Quantum Einstein Gravity
• Nonperturbative quark matter equations of state with vector interactions
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• Randomly dilute Ising model: A nonperturbative approach
• Scaling behavior of impurities in mesoscopic Luttinger liquids
• Thermodynamic phases and mesonic fluctuations in a chiral nucleon-meson model
• Five-loop epsilon expansion for O(n)xO(m) spin models
• Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks
• A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories
• A Safe Beginning for the Universe?
• The Planck scale, the Higgs mass and scalar dark matter
• Non-Perturbative Renormalization Group Analysis of the Chiral Critical Behaviors in QED
• A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections
• Safety in darkness: Higgs portal to simple Yukawa systems
• Critical Phenomena in Continuous Dimension
• Asymptotic Safety, Singularities, and Gravitational Collapse
• Functional renormalization for trion formation in ultracold fermion gases
• Renormalization group methods and the 2PI effective action
• Gauge-invariant fields and flow equations for Yang-Mills theories
• Renormalization group flow of Hořava-Lifshitz gravity at low energies
• Non-perturbative states in the 3D phi^4 theory
• Quantum gravity with torsion and non-metricity
• Global flow of the Higgs potential in a Yukawa model
• Influence of quark boundary conditions on the pion mass in finite volume
• Polyakov Effective Action from Functional Renormalization Group Equation
• Quantum Gravity: A Brief History of Ideas and Some Prospects
• Luttinger liquid properties of the steady state after a quantum quench
• Criticality of the random field Ising model in and out of equilibrium: a nonperturbative functional renormalization group description
• Non-thermal fixed points: Universal dynamics far from equilibrium
• BRS symmetry from renormalization group flow
• Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model
• PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Fixed point structure of the conformal factor field in quantum gravity
• The generalised infrared structure of the gluon propagator
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Effective Quark Interactions and QCD-Propagators
• One loop beta functions and fixed points in Higher Derivative Sigma Models
• The "tetrad only" theory space: Nonperturbative renormalization flow and Asymptotic Safety
• On the impact of Majorana masses in gravity-matter systems
• The effective potential of the confinement order parameter in the Hamilton approach
• Functional renormalization group analysis of the soft mode at the QCD critical point
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• Phase structure of spin-imbalanced unitary Fermi gases
• Renormalization group study of the four-body problem
• Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability
• Non-perturbative renormalization-group approach to zero-temperature Bose systems
• Fierz-complete NJL model study II: towards the fixed-point and phase structure of hot and dense two-flavor QCD
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Exact scheme independence at two loops
• Three-body scattering from nonperturbative flow equations
• Quantum scale symmetry
• Infinite order quantum-gravitational correlations
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• First order phase transitions in polymerized phantom membranes
• Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model
• Gauge invariant regularisation via SU(N|N)
• The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
• Properties of multi-particle Green and vertex functions within Keldysh formalism
• Monopoles, Polyakov-Loops and Gauge Fixing on the Torus
• Non-perturbative QEG Corrections to the Yang-Mills Beta Function
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• On the construction of renormalized gauge theories using renormalization group techniques
• Random Tensors and Quantum Gravity
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Superfluid Bose gas in two dimensions
• Constraining the Asymptotically Safe Cosmology: cosmic acceleration without dark energy
• Global Wilson-Fisher fixed points
• Functional renormalization group approach to interacting bosons at zero temperature
• Correlating the skewness and kurtosis of baryon number distributions
• Price of Asymptotic Safety
• Correlation effects on resonant tunneling in one-dimensional quantum wires
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Localization of Elastic Layers by Correlated Disorder
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Functional renormalization group approach and gauge dependence in gravity theories
• Signatures of Primordial non-Gaussianities in the Matter Power-Spectrum and Bispectrum: the Time-RG Approach
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Nonlocal effective average action approach to crystalline phantom membranes
• The Strongly Interacting Electroweak Phase Transition
• Renormalization of the BCS-BEC crossover by order parameter fluctuations
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Essential nature of Newton's constant in unimodular gravity
• Bound state properties from the Functional Renormalisation Group
• Exact scheme independence at one loop
• Exact Flow Equations and the U(1)-Problem
• Functional renormalization group study of the Quark-Meson model with $\omega$ meson
• Modified Fermi-sphere, pairing gap and critical temperature for the BCS-BEC crossover
• Kardar-Parisi-Zhang universality in the phase distributions of one-dimensional exciton-polaritons
• Exact renormalization group for quantum spin systems
• Composite Operators in Asymptotic Safety
• Asymptotic safety and the cosmological constant
• The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Exact renormalization group and Phi-derivable approximations
• Quantum-mechanical tunnelling and the renormalization group
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Background Scale Independence in Quantum Gravity
• Net quark number probability distribution near the chiral crossover transition
• Confinement order parameters and fluctuations
• Scheme Independence at First Order Phase Transitions and the Renormalisation Group
• The unitary conformal field theory behind 2D Asymptotic Safety
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion
• DoFun 3.0: Functional equations in Mathematica
• Exact RG Flow Equations and Quantum Gravity
• Coleman-Weinberg Phase Transition in Two-Scalar Models
• Fixed points and the spontaneous breaking of scale invariance
• Asymptotic safety of gravity, the Higgs boson mass and beyond the Standard Model physics
• Consistent early and late time cosmology from the RG flow of gravity
• Critical Discussion of the 2-Loop Calculations for the KPZ-Equation
• Universal aspects of the phase diagram of QCD with heavy quarks
• Yang-Mills correlators across the deconfinement phase transition
• A non perturbative approach of the principal chiral model between two and four dimensions
• Spatiotemporal velocity-velocity correlation function in fully developed turbulence
• High Temperature Phase Transition in Two-Scalar Theories
• Quark and Nuclear Matter in the Linear Chiral Meson Model
• Flow Equation for Supersymmetric Quantum Mechanics
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Critical $O(N)$ models in the complex field plane
• Gravitational antiscreening in stellar interiors
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• Singularity free gravitational collapse in an effective dynamical quantum spacetime
• Predictive power of grand unification from quantum gravity
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
• Gauge invariance of the background average effective action
• Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
• Rotation Symmetry Breaking Condensate in a Scalar Theory
• Asymptotic safety and the gauged SU(N) nonlinear sigma-model
• Optimization of field-dependent nonperturbative renormalization group flows
• Fully developed isotropic turbulence: symmetries and exact identities
• Splitting Ward identity
• Confinement in Polyakov Gauge
• Asymptotic safety with Majorana fermions and new large N equivalences
• Curvature dependence of quantum gravity with scalars
• New developments in lattice QCD on equilibrium physics and phase diagram
• Geometrical effective action and Wilsonian flows
• The Chiral Phase Transition at High Baryon Density from Nonperturbative Flow Equations
• Scheme dependence and universality in the functional renormalization group
• Scalegenesis and fermionic dark matters in the flatland scenario
• Critical temperature and superfluid gap of the Unitary Fermi Gas from Functional Renormalization
• Manifestly gauge invariant QED
• Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations
• Universality and symmetry breaking in conformally reduced quantum gravity
• Non-Singular Black Holes, the Cosmological Constant and Asymptotic Safety
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Equation of state near the endpoint of the critical line
• Gluon condensation and scaling exponents for the propagators in Yang-Mills theory
• On Gauge Invariant Wilsonian Flows
• Cluster Functional Renormalization Group
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• A curvature bound from gravitational catalysis
• How to Wick rotate generic curved spacetime
• Calculations of the dynamical critical exponent using the asymptotic series summation method
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Scaling functions for the O(4)-model in d=3 dimensions
• The Region of Validity of Homogeneous Nucleation Theory
• Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory
• Phase Diagram and Fixed-Point Structure of two dimensional N=1 Wess-Zumino Models
• Non-perturbative dynamics and charge fluctuations in effective chiral models
• Global surpluses of spin-base invariant fermions
• Flow Equations for the Higgs Top System
• Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
• Fermions and Goldstone bosons in an asymptotically safe model
• Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
• Scaling and superscaling solutions from the functional renormalization group
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group
• Non-linear matter power spectrum from Time Renormalisation Group: efficient computation and comparison with one-loop
• Strangeness Neutrality and QCD Thermodynamics
• An Exact Renormalization Group analysis of 3-d Well Developed turbulence
• On the ERG approach in $3-d$ Well Developed Turbulence
• Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking
• Effective interactions and fluctuation effects in spin-singlet superfluids
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• Dynamic universality class of Model C from the functional renormalization group
• Three-body loss in lithium from functional renormalization
• Finite-density QCD transition in magnetic field background
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Volume dependence of baryon number cumulants and their ratios
• Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Finite-Temperature Gluon Condensate with Renormalization Group Flow Equations
• Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field
• Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group
• Split Weyl transformations in quantum gravity
• Two-particle irreducible functional renormalization group schemes---a comparative study
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions
• The non-perturbative renormalization group in the ordered phase
• Four-point vertex in the Hubbard model and partial bosonization
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Renormalization Group Studies of Dense Relativistic Systems
• Charge cross-over at the U(1)-Higgs phase transition
• Emergent Hadrons and Diquarks
• Role of mesonic fluctuations in the Polyakov loop extended quark-meson model at imaginary chemical potential
• Two-loop beta-function from the exact renormalization group
• A non-perturbative renormalization group study of the stochastic Navier--Stokes equation
• Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
• Massive Yang-Mills Theory in Abelian Gauges
• Phase structure of NJL model with weak renormalization group
• Infrared limit of quantum gravity
• A note on scaling arguments in the effective average action formalism
• BRST in the Exact RG
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Bosonic effective action for interacting fermions
• Finite-Size Scaling behavior in the O(4)-Model
• Are there scaling solutions in the O(N)-models for large N in d>4?
• Spin-base invariance of Fermions in arbitrary dimensions
• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• Entropy Production during Asymptotically Safe Inflation
• Functional renormalization group approach to the Yang-Lee edge singularity
• Ward identity violation for melonic $T^4$-truncation
• Fermionic spectral functions with the Functional Renormalization Group
• Time-evolution of fluctuations as signal of the phase transition dynamics in a QCD-assisted transport approach
• Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• A functional perspective on emergent supersymmetry
• Flowing with the Temporal Renormalisation Group
• Renormalization in periodically driven quantum dots
• Asymptotic safety and Conformal Standard Model
• Low-energy limit of the $O(4)$ quark-meson model from the functional renormalization group approach
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies
• Nonperturbative thermodynamics of an interacting Bose gas
• Vanishing Beta Function curves from the Functional Renormalisation Group
• Non-Perturbative Renormalization Group for Simple Fluids
• Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry
• A bootstrap strategy for asymptotic safety
• Critical behavior of supersymmetric O(N) models in the large-N limit
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Supersymmetry breaking as a quantum phase transition
• Universality in antiferromagnetic strange metals
• Asymptotically safe gravity
• N=1 Wess Zumino Model in d=3 at zero and finite temperature
• Quantum gravity effects in Myers-Perry space-times
• Baryon number fluctuations in the 2+1 flavor low energy effective model
• Strangeness neutrality and baryon-strangeness correlations
• Covariant and background independent functional RG flow for the effective average action
• Renormalization-group flow of the effective action of cosmological large-scale structures
• A glassy phase in quenched disordered graphene and crystalline membranes
• Exact Symmetries realized on the Renormalized Group Flow
• Bubble-nucleation rates for radiatively induced first-order phase transitions
• Asymptotically free scaling solutions in nonabelian Higgs models
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD
• Functional renormalization group approach to non-collinear magnets
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• Functional Renormalization for Chiral and U_A(1) Symmetries at Finite Temperature
• Spontaneous symmetry breaking and optimization of functional renormalization group
• Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
• Tachyonic instability of the scalar mode prior to QCD critical point based on Functional renormalization-group method
• Gauge-Invariant Renormalization Group at Finite Temperature
• Excitonic instability and unconventional pairing in the nodal-line materials ZrSiS and ZrSiSe
• Integrating out Gluons in Flow Equations
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills
• C Function Representation of the Local Potential Approximation
• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• Nonabelian Higgs models: paving the way for asymptotic freedom
• The flat phase of quantum polymerized membranes
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• Gauge Consistent Wilson Renormalization Group I: Abelian Case
• Nonequilibrium thermoelectric transport through vibrating molecular quantum dots
• Renormalization group flow equations connected to the $n$PI effective action
• Thermodynamics of the two-dimensional XY model from functional renormalization
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Phases of supersymmetric O(N) theories
• Functional renormalization group of the non-linear sigma model and the O(N) universality class
• On Exact Proper Time Wilsonian RG Flows
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations
• Nonperturbative renormalization-group approach to fermion systems in the two-particle-irreducible effective action formalism
• Renormalization group flow of the Luttinger-Ward functional: conserving approximations and application to the Anderson impurity model
• Topological Susceptibility in Three-Flavor Quark Meson Model at Finite Temperature
• The fate of non-polynomial interactions in scalar field theory
• Covariant and single-field effective action with the background-field formalism
• QCD-inspired determination of NJL model parameters
• Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at $T>0$
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach
• Trace anomaly and infrared cutoffs
• From Asymptotic Safety to Dark Energy
• Kardar-Parisi-Zhang Equation with temporally correlated noise: a non-perturbative renormalization group approach
• Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations
• Localized rainbows in the QCD phase diagram
• Activated dynamic scaling in the random-field Ising model: a nonperturbative functional renormalization group approach
• Non-perturbative renormalization group calculation of the quasi-particle velocity and the dielectric function of graphene
• Non-Perturbative Renormalization Group for the Diffusive Epidemic Process
• On the 2-point function of the O(N) model
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover
• Confinement, Monopoles and Wilsonian Effective Action
• Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization
• Scaling relations and multicritical phenomena from Functional Renormalization
• Scaling solutions in the derivative expansion
• A new functional flow equation for Einstein-Cartan quantum gravity
• On the construction of QED using ERG
• Gauge Consistent Wilson Renormalization Group II: Non-Abelian Case
• Convexity of the effective action from functional flows
• The Exact Renormalization Group -- renormalization theory revisited --
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Fractal geometry of higher derivative gravity
• Renormalization in Condensed Matter: Fermionic Systems - from Mathematics to Materials
• Axial anomalies in gauge theory by exact renormalization group method
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Wilsonian Flow and Mass-Independent Renormalization
• Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid
• Mesonic dynamics and QCD phase transition
• Renormalization group in the internal space
• Functional renormalization group for quantized anharmonic oscillator
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Geometric operators in the asymptotic safety scenario for quantum gravity
• One Loop Beta Functions in Topologically Massive Gravity
• Weak solution of the non-perturbative renormalization group equation to describe the dynamical chiral symmetry breaking
• Products of composite operators in the exact renormalization group formalism
• Evaporation of (quantum) black holes and energy conservation
• RG flow equations for the proper-vertices of the background effective average action
• Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy
• Dynamical generation of low-energy couplings from quark-meson fluctuations
• Low energy singularities in the ground state of fermionic superfluids
• Functional Renormalization of Noncommutative Scalar Field Theory
• Phase Transitions in liquid Helium 3
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
• Scheme independence as an inherent redundancy in quantum field theory
• The ordered phase of $O(N)$ model within the Non-Perturbative Renormalization Group
• Non-perturbative renormalization-group approach to lattice models
• Asymptotically Safe Non-Minimal Inflation
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• A functional RG equation for the c-function
• Effects of the Running of the QCD Coupling on the Energy Loss in the Quark-Gluon Plasma
• Ward-constrained melonic renormalization group flow
• In-medium spectral functions and dilepton rates with the Functional Renormalization Group
• Evolution of cosmological perturbations in an RG-driven inflationary scenario
• Sarma phase in relativistic and non-relativistic systems
• Universal behavior of coupled order parameters below three dimensions
• Effective Average Action in N=1 Super-Yang-Mills Theory
• Quantum Master Equation for QED in Exact Renormalization Group
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
• General Computations Without Fixing the Gauge
• Could reggeon field theory be an effective theory for QCD in the Regge limit?
• Fluctuating vector mesons in analytically continued FRG flow equations
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Structure of the broken phase of the sine-Gordon model using functional renormalization
• Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
• Functional renormalization group study of the critical region of the quark-meson model with vector interactions
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• Operator product expansion coefficients in the exact renormalization group formalism
• Critical exponents in quantum Einstein gravity
• Resolving phase transitions with Discontinuous Galerkin methods
• Renormalization group, dimer-dimer scattering, and three-body forces
• Some exact results in branching and annihilating random walks
• BRST invariant RG flows
• Baryon number probability distribution at finite temperature
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• Relativistic BEC extracted from a complex FRG flow equation
• Subtleties in the calculation of correlation functions for hot and dense systems
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Vertex functions and their flow equations from the 2PI effective action
• Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific
• Universal amplitudes ratios for critical aging via functional renormalization group
• Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Fate of chiral symmetry in Riemann-Cartan geometry
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function
• Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling
• Spin functional renormalization group for dimerized quantum spin systems
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Renormalisation of non-differentiable potentials
• Gribov copies in the quark propagator
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes
• Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures
• Spin bond order driven by extended repulsive interactions in doped graphene
• 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
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group
• The $\theta$-vacuum from functional renormalisation
• New universality classes govern the critical and multicritical behavior of an active Ising model
• Non-Perturbative $S$-matrix Renormalization
• Charting GLOBs in Asymptotically Safe Gravity
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids
• 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
• 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
• The effect of charm quark on the QCD chiral phase diagram
• Stability of ${\phi }^4$-vector model: four-loop $\epsilon$ expansion study
• Basic properties of an alternative flow equation in gravity theories
• Exact generating function of a zero-dimensional supersymmetric non-linear sigma model
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds