Perfect lattice action for asymptotically free theories

Abstract

There exist lattice actions which give cut--off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant instanton solutions. This perfect action can be made short ranged. It can be determined by combining analytical calculations with numerical simulations on small lattices. We illustrate the method and the benefits on the $d=2$ non--linear $\sigma$--model.

29 pages(part 1) + 9 postscript figures(part 2, compressed by uufiles). No changes, replaced due to transmission error observed, BUTP-93/17

Cited by in corpus (239)

• Thermodynamics of SU(3) Lattice Gauge Theory
• QCD forces and heavy quark bound states
• The index theorem in QCD with a finite cut-off
• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
• Massive Fermions in Lattice Gauge Theory
• Fundamentals of the Exact Renormalization Group
• Lattice QCD without tuning, mixing and current renormalization
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Prospects for perfect actions
• Perfect Lattice Actions for Quarks and Gluons
• Light Hadron Masses from Lattice QCD
• The classically perfect fixed point action for SU(3) gauge theory
• Topology of the SU(2) vacuum: a lattice study using improved cooling
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Improved and Perfect Actions in Discrete Gravity
• Staggered eigenvalue mimicry
• A continuum limit of the chiral Jacobian in lattice gauge theory
• Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly
• Renormalization group flow of SU(3) lattice gauge theory - Numerical studies in a two coupling space
• Testing the fixed-point QCD action and the construction of chiral currents
• Coarse graining methods for spin net and spin foam models
• Meson and baryon spectrum for QCD with two light dynamical quarks
• Quenched spectroscopy with fixed-point and chirally improved fermions
• Non--perturbative tests of the fixed point action for SU(3) gauge theory
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• Perfect discretization of reparametrization invariant path integrals
• A variant approach to the overlap action
• Topological Structure in the SU(2) Vacuum
• Lattice Quantum Gravity and Asymptotic Safety
• Nucleon Properties from Unconventional Interpolating Fields
• The QCD vacuum
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Hadron Spectroscopy with Dynamical Chirally Improved Fermions
• Perfecting the Ultra-violet of Holographic Descriptions of QCD
• Machine learning action parameters in lattice quantum chromodynamics
• Topological susceptibility in full QCD with Ginsparg-Wilson fermions
• Supersymmetry on the lattice
• Time evolution as refining, coarse graining and entangling
• Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator
• A Perturbative Construction of Lattice Chiral Fermions
• Simple Observables from Fat Link Fermion Actions
• Revealing Topological Structure in the SU(2) Vacuum
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Solutions to the reconstruction problem in asymptotic safety
• Instantons and Fixed Point Actions in SU(2) Gauge Theory
• Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models
• Universality and scaling behavior of RG gauge actions
• Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
• Axial vector current of exact chiral symmetry on the lattice
• Fixed point action for the massless lattice Schwinger model
• A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
• Fixed Point Gauge Actions with Fat Links: Scaling and Glueballs
• Progress on Perfect Lattice Actions for QCD
• Meson and Baryon dispersion relations with Brillouin fermions
• Topological Lattice Actions
• Improved Actions for QCD Thermodynamics on the Lattice
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Fixed point actions for SU(3) gauge theory
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Algorithms for Lattice QCD with Dynamical Fermions
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• The absence of cut--off effects for the fixed point action in 1--loop perturbation theory
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Chiral properties of two-flavor QCD in small volume and at large lattice spacing
• Convergence Rate and Locality of Improved Overlap Fermions
• Redesigning Lattice QCD
• Towards a Perfect QCD Gravity Dual
• Improved Lattice Gauge Field Hamiltonian
• Renormalization of bilinear quark operators for the chirally improved lattice Dirac operator
• Brillouin improvement for Wilson fermions
• Fixed Point Action and Topology in the CP^3 Model
• New fixed point action for SU(3) lattice gauge theory
• Triviality and the Higgs mass lower bound
• Leptonic Decays of Heavy Quarks on the Lattice
• Relation $Tr{\gamma }_5=0$ and the index theorem in lattice gauge theory
• Perfect Actions with Chemical Potential
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Dynamical Fermions with Fat Links
• Triviality from the Exact Renormalization Group
• Topology and chiral symmetry breaking in SU(N) gauge theories
• Lattice calculation of low energy constants with Ginsparg-Wilson type fermions
• Tests of Hypercubic Fermion Actions
• Is the 2D O(3) Nonlinear $\sigma$ Model Asymptotically Free?
• Perfect Lattice Actions for Staggered Fermions
• Perfect Lattice Actions for the Gross-Neveu Model at large N
• Fixed-point action for fermions in QCD
• Simulating Full QCD with the Fixed Point Action
• Improved lattice actions
• On the question of universality in $\RPn$ and $\On$ Lattice Sigma Models
• Unexpected results in asymptotically free quantum field theories
• The effect of tree-level and mean-field improvement on the light-hadron spectrum in quenched QCD
• Optimal Renormalization Group Transformation from Information Theory
• Lattice 2001: Reflections
• Gauge Field Strength Tensor from the Overlap Dirac Operator
• Effective lattice theories for Polyakov loops
• Quark Hadron Duality at Finite Temperature
• Thermodynamics of Lattice QCD with Chiral 4-Fermion Interactions
• Canonical Demon Monte Carlo Renormalization Group
• Perfect Lattice Topology: The Quantum Rotor as a Test Case
• Global obstructions to gauge-invariance in chiral gauge theory on the lattice
• QCD with two dynamical flavors of chirally improved quarks
• Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
• Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Exact Chiral Symmetry on the Lattice: QCD Applications
• Preconditioning of Improved and ``Perfect'' Fermion Actions
• Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential
• Quenched QCD with fixed-point and chirally improved fermion
• Renormalization group and perfect operators for stochastic differential equations
• Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance
• Chiral properties of the fixed point action of the Schwinger model
• Block Spins for Partial Differential Equations
• Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model
• Computation of the one-loop Symanzik coefficients for the square action
• The Intrinsic Coupling in Integrable Quantum Field Theories
• On-shell improved lattice QCD with staggered fermions
• Locality Properties of a New Class of Lattice Dirac Operators
• Questionable and unquestionable in the perturbation theory of non-Abelian models
• A Numerical Study of the 2-Flavour Schwinger Model with Dynamical Overlap Hypercube Fermions
• Fixed-Point Actions in 1-Loop Perturbation Theory
• Recent results from systematic parameterizations of Ginsparg-Wilson fermions
• Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
• Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature
• Asymptotically free theories based on discrete subgroups
• Renormalization group flow and fixed point of the lattice topological charge in the 2-d O(3) sigma-model
• Instanton size distribution in O(3)
• A lattice calculation of the pion form factor with Ginsparg-Wilson-type fermions
• Topological structure in the SU(2) vacuum
• Towards Weyl fermions on the lattice without artefacts
• Action and topological density carried by Abelian monopoles in finite temperature pure SU(2) gauge theory: an analysis using RG smoothing
• On the Renormalization of Theories of a Scalar Chiral Superfield
• Questionable Arguments for the Correctness of Perturbation Theory in Non-Abelian Models
• Anti-Ferromagnetic Condensate in Yang-Mills Theory
• Classical improvement of lattice actions and quantum effects: a unified view
• A Resummable beta-Function for Massless QED
• Noisy Monte Carlo revisited
• Perfect Scalars on the Lattice
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• Perfect Lattice Actions with and without Chiral Symmetry
• Monopole characteristics in various Abelian gauges
• The Schwinger Model with Perfect Staggered Fermions
• Chiral gauge theories on the lattice with exact gauge invariance
• Topological aspects of QCD
• Yang-Mills Theory In Axial Gauge
• Meson spectral functions with chirally symmetric lattice fermions
• Lattice Regularization and Symmetries
• On the index theorem for Wilson fermions
• Scaling and topology in the 2-d O(3) $\sigma$-model on the lattice with the fixed point action
• The fixed point action for the Schwinger model: a perturbative approach
• Thermodynamics of the two--dimensional O(3) non linear sigma model with Fixed-Point lattice action
• Thermodynamical quantities of lattice full QCD from an efficient method
• Comparing Different Improvement Programs for the N-Vector Model
• Verification of O(a) improvement
• Steps towards Lorentzian quantum gravity with causal sets
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Axial Anomaly and Index of the Overlap Hypercube Operator
• Absence of evidence for pentaquarks on the lattice
• Improved actions and asymptotic scaling in lattice Yang-Mills theory
• New overlap construction of Weyl fermions
• Towards a perfect fixed point action for SU(3) gauge theory
• Perfect topological charge for asymptotically free theories
• Six-dimensional regularization of chiral gauge theories
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
• A renormalisation group derivation of the overlap formulation
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Scope and convergence of the hopping parameter expansion in finite temperature QCD with heavy quarks around the critical point
• The Hadron Spectrum from Lattice QCD
• QCD for Coarse Lattices
• Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
• Instanton classical solutions of SU(3) fixed point actions on open lattices
• Fixed Point SU(3) Gauge Actions: Scaling Properties and Glueballs
• SSOR Preconditioning of Improved Actions
• Classically Perfect Gauge Actions on Anisotropic Lattices
• A Real Space Renormalization Group Approach to Field Evolution Equations
• Brief Review of Saturation Physics
• Two Lectures on QCD at Short Distances: Jets and Factorization
• Perfect Lattice Perturbation Theory: A Study of the Anharmonic Oscillator
• Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit
• Bound states for Overlap and Fixed Point Actions close to the chiral limit
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• An Improved Single-Plaquette Gauge Action
• Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory
• New solutions to the Ginsparg-Wilson equation
• Criticality of the (2+1)-dimensional S=1 transverse-field Ising model with extended interactions: Suppression of corrections to scaling
• Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results
• Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
• The Shape of the Renormalized Trajectory in the Two-dimensional O(N) Non-linear Sigma Model
• Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials
• Noisy Monte Carlo Algorithm
• Renormalization group improved action on anisotropic lattices
• Cluster algorithms
• Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory
• Renormalization factors of quark bilinears using the DCI operator with dynamical quarks
• Properties of Renormalization Group Transformations
• Double expansion in asymptotically free theories
• A New Lattice Action for Studying Topological Charge
• A new approach to instanton calculations in the O(3) nonlinear sigma model
• Impossibility of spontaneous vector flavor symmetry breaking on the lattice
• A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature
• Quantum lattice models that preserve continuous translation symmetry
• Exclusive Decays of Beauty Hadrons
• Zeroes in the Complex Beta Plane Of 2D Ising Block Spin Boltzmannians
• A Preconditioner for Improved Fermion Actions
• Scaling Analysis of Improved Actions for Pure SU(3) Gauge Theory
• Canonical Demon Monte Carlo Renormalization Group
• Corrections to finite-size scaling in two-dimensional O(N) sigma-models
• Improved actions, the perfect action, and scaling by perturbation theory in Wilsons renormalization group: the two dimensional $O(N)$-invariant non linear $\sigma$-model in the hierarchical approximation
• Improving the signal-to-noise-ratio in lattice gauge theories
• The Perfect Laplace Operator for Non-Trivial Boundaries
• 1-Loop improved lattice action for the nonlinear sigma-model
• The fixed point action of the Schwinger model
• A fixed-point action for the lattice Schwinger model
• The Schwinger Model with Perfect Staggered Fermions
• Testing the efficiency of different improvement programs
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• Perfect Gauge Actions on Anisotropic Lattices
• d=2 transverse-field Ising model under the screw-boundary condition: An optimization of the screw pitch
• LATTICE QCD AND THE STANDARD MODEL
• Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
• Variational Study of the Phase Transition at Finite T in the $\lambda {\varphi }^4$-Theory
• Holography of Strongly Coupled Gauge Theories
• Improved actions for the two-dimensional sigma-model
• Perfect discretization of path integrals
• Modified Abelian and SU(2) Wilson theories on a lattice from a non-compact regularization
• The Renormalized Trajectory of the O(N) Non-linear Sigma Model
• Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
• Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model
• Monte Carlo Renormalization Group analysis of QCD in two dimensional coupling space
• Comparing lattice Dirac operators with Random Matrix Theory
• The Renormalization Group and its Finite Lattice Approximations
• Perfect Lattice Actions for the Gross-Neveu Model
• Improving QCD with fermions: the 2 dimensional case of QCD with Sea Quarks
• Scaling topological charge in the CP^3 model using a fixed point action
• Abelian monopoles in finite temperature lattice gauge fields: Classically perfect action, smoothing and various Abelian gauges
• Fixed point actions in SU(3) gauge theory: surface tension and topology